AVA Cambridge 2000, Basic Physics and Measurement: THE GAS LAWS
THE GAS LAWS
Some aspects of their importance in anaesthesia
Presentation: Yves Moens, DVM, PhD, Dipl. ECVA
1.
2.
3.
4.
5.
6.
7.
8.
Molecular theory
The gas laws
Adiabatic changes
Dalton’s law of partial pressures
Avogadro’s hypothesis
Universal gas constant
Critical temperature
Dalton’s law , barometric pressure and water vapour
Some References:
1. Basic Physics and Measurement in Anaesthesia; Davis, Parbrook and Kenny;
Butterworth-Heineman, 4th edition.
2. All you really need to know to interpret arterial blood gases; Lawrence Martin; Lea and
Febiger, 1992.
3. Water vapor calibration errors in some capnometers: respiratory conventions
misunderstood by manufacturers? John W. Severinghaus, Anesthesiology 70; 996-998,
1989.
4. Physics applied to anaesthesia, third ed., ISBN 0407 00399.
5. Textbook of Medical Physiology; Arthur C. Guyton; 6thed., WB Saunders.
6. Anesthetic considerations at moderate altitude. MF James, JF White; Anesth Analg
63;1097-1105, 1984.
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1. MOLECULAR THEORY
A brief review of molecular theory is given first because it is a help in understanding
the gas laws.
All substances are composed of atoms or compounds of atoms, i.e. molecules. In a
solid, the atoms or molecules are usually arranged in a regular formation called a
lattice and each molecule in the lattice exerts forces on its neighbours and is
continuously in motion, oscillating about a mean position. ff heat is added to a solid,
each molecule vibrates with a greater amplitude and therefore takes up a greater
amount of space. The molecules move further apart and consequentIy the force
exerted by each on its neighbours is reduced. Eventually the forces are not sufficient
to hold the molecules in a lattice although smaller groupings remain. The lattice
breaks down, the substance melts, and turns into a liquid. In a liquid the molecules
still exert some influence on each other and the forces of attraction between them are
called Van der Waals' forces. The molecules in a liquid have more vibrational energy
than in a solid and each one can move about through the liquid. If heat is added to a
liquid, each molecule gains further kinetic energy and eventually some are able to
overcome the Van der Waals' forces exerted by their neighbours and are able to
move about in space. This state is that of a gas or vapour .
Figure 1 illustrates the interface between a liquid and its vapour. Molecules at the
surface of the liquid occasionally escape, as shown at 'A’
Figure 1 : Interface between a liquid and a gas.
in the diagram. Conversely, molecules of gas moving towards the liquid may transfer
into the liquid phase, as shown at 'B'. Eventually, at any one temperature an
equilibrium occurs between these two rates of molecular transfer and the vapour
above the liquid is said to be saturated.
li the liquid is heated to its boiling point, the energy of the molecules is so great that
they all transfer to the gaseous phase. In a gas, the molecules collide with each other
and with the walls of a container at frequent intervals. The result of the collisions
between the molecules of a gas and the walls of the container is that a force is
exerted on the walls, and this force exerted over a certain area is defined as the
pressure.
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2. THE GAS LAWS
Figure 2 illustrates a volume of gas within a large syringe. The collisions between the
molecules and the walls of the container result in an absolute pressure P, which in
this case is a typical atmospheric pressure of 100 kPa (1 bar). If this syringe is at a
constant temperature, the molecules will have a certain energy of motion and will
therefore collide with the walls of the container at a given frequency.
Absolute pressure p
Figure 2: Gas in a syringe model to illustrate molecular theory.
If the temperature is kept constant and the volume of the container is reduced
(Fig. 3), the molecules will still have the same energy of motion but, as they are in a
smaller volume, they will collide with the walls of the container more frequently. The
greater the number of collisions with the walls, the greater the pressure of the gas in
the container. Halving the volume V of the syringe, as in Fig. 3, doubles the absolute
pressure p from 100 to 200 kPa.
Figure 3: Effect of volume change at constant temperature.
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V∝
1
P
PV = Cons tan t (k1 )
This is the first perfect gas law, Boyle's law. This weIl known gas law was first
published by the Hon. Robert Boyle in 1662.
Boyle's law states that at constant temperature the volume of a
given mass of gas varles inversely with the absolute pressure.
Figure 4 provides an example of the application of Boyle's law. On the lef t is shown
a typical large oxygen cylinder such as is used in oxygen therapy. How much oxygen
will be available at atmospheric pressure? The internal capacity of the cylinder is
about 10 litres and when full it has a gauge pressure of 137 bar or 13 700 kPa. If the
atmospheric pressure is 100 kPa, the total or absolute pressure of the oxygen will be
13 800 kPa, since absolute pressure is gauge pressure plus atmospherlc pressure.
The calculations are given on the right of the diagram and the total volume of oxygen
works out at 1380 litre. As 10 litre are retained in the 'empty' oxygen cylinder, 1370
litre are available for delivery at atmospheric pressure.
Figure 4: Use of Boyle's law to calculate the content of an oxygen cylinder.
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Consider now a gas maintained at constant pressure (Fig. 5). In the
example shown, this means that the barrel of the syringe is allowed to move freely to
maintain the ambient pressure of 100 kPa. If heat is added to the volume of gas, as
in the lower diagram, the energy of movement of the molecules increases and this
results in more collisions with the walls of the container. In order that the frequency of
collisions, and thus the pressure, remains constant the volume must increase. Thus,
if the absolute temperature T in the syringe is doubled from 273 K to 546 K, it is
found that the volume V in the syringe also doubles.
Figure 5: Effect of temperature change at constant pressure
V ∝T
V
= Cons tan t (k2 )
T
This is the second perfect gas law and is due to the Frenchman Jacques Charles.
Charles's law states that at constant pressure the volume of a given mass of
gas varies directIy with the absolute temperature.
This law shows that gases expand when they are heated and so become less dense.
It means too that warm air tends to rise and this causes convection currents.
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The third of the gas laws is illustrated in Fig. 6 in which a syringe is maintained at
constant volume. If heat is added to this constant-volume container, the molecules of
the gas gain kinetic energy and collide with the walls of the container more
frequently, thus resulting in an increase in pressure. Consequently, at constant
volume, a change in absolute temperature T in a gas produces a change in pressure
P.
Figure 6: Effect of temperature change at constant volume.
P ∝T
P
= Cons tan t (k3 )
T
The third perfect gas law states that at constant volume the absolute pressure
of a given mass of gas varles directIy with the absolute temperature.
As an example of this law, consider an oxygen cylinder filled to an absolute pressure
of 138 bar at an ambient temperature of 290 K (17°C). Cylinders are tested to
withstand pressures of up to 210 bar. If the cylinder is dropped accidentally into an
incinerator at 580 K (307°C), is there a danger of explosion of the cylinder from the
pressure increase? A doubling of the absolute temperature doubles the pressure,
thus the pressure in the cylinder increases to over 210 bar. The cylinder is likely to
explode even if the weakening of the metal of the cylinder by the heat is ignored.
Another example of this law is the hydrogen thermometer, used as a standard for
scientific temperature measurement. When a constant volume
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of hydrogen is heated, the rise in pressure may be accurately recorded and it gives a
measure of the absolute temperature increase.
As volumes of gases are greatly affected by changes of temperature and
pressure, it is important to specify the temperature and pressure at which any
measurement of volume is made. Moreover, it is often useful to correct results to a
standard temperature and pressure. The standard temperature used is 273.15 K
(O°C), and the standard pressure 101.325 kPa (760 mmHg). This standard
temperature and pressure is known as s.t.p. (see later).
3. ADIABATIC CHANGES OF STATE IN A GAS
The three gas laws describe the behaviour of a gas when one of the three variables,
pressure, temperature or volume is constant. For these conditions to apply, heat
energy is required to be added to or taken from a gas as the change occurs.
The state of a gas can also be altered without allowing the gas to exchange heat
energy with its surroundings, and this is called an adiabatic change. An example of
such a change occurs when air is compressed in an air supply unit; the gas is
compressed adiabatically and the temperature of the air rises and so a system of
cooling is needed.
Altematively, if a compressed gas expands adiabatically,cooling occurs as in the
cryoprobe .The cryoprobe is used for rapid freezing of tissues in the treatment of skin
lesions, in gynaecology, and in ophthalmic surgery. The elements of a typical
cryoprobe are shown in Fig.4.7. Gas is allowed to expand rapidly out of a capillary
tube and a fall in temperature occurs as a result of the expansion. The cooling effect
arises from the fact that energy is required as a gas expands to overcome the Van
der Waals' forces of attraction between the molecules of the gas. In a rapid
expansion, heat exchange does not take place between the gas and its
surroundings, so the energy required comes from the kinetic energy of the gas
molecules themselves which results in the gas cooling as it expands. Nitrous oxide or
carbon dioxide is a suitable gas and the gas flows from the cylinder through an
adjustable pressure regulator which may be used to set the cooling rate. The gas
flows through a capillary tube in the cryoprobe and expands in the probe tip where a
temperature as low as -70°C may be produced.
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4. DALTON'S LA W OF PARTlAL PRESSURES
Figure 8 illustrates a mixture of gases in a container. Pressure in the container is
related to the frequency of collisions and to the mass and velocity of the molecules of
the gas. In a mixture, each type of molecule contributes to the pressure exerted on
the walls of the container and because each molecule behaves almost independently
of its neighbours the pressure attributable to any one type of molecule is the same
whether the other type of molecule is present or not.
Figure 8: gas mixture in a container
This phenomenon was first established by John Dalton and is known as Dalton's law
of partial pressures.
Dalton's law of partial pressures states that in a mixture of gases the pressure
exerted by each gas is the same as that which it would exert if it alone
occupied the container .
In anaesthesia the partial pressures of gases in a mixture are often of
interest.
The left of Fig. 9 illustrates an Entonox cylinder emptied to an ambient pressure of
100 kPa (750 mmHg). The mixture remaining in the cylinder is 50% nitrous oxide,
50% oxygen and so each gas occupies half the cylinder volume. According to
Dalton's law, the pressure exerted by the nitrous oxide in the cylinder is the same as
it would exert if it alone occupied the container. But if it were to do this, the available
space for the nitrous oxide would have increased from half the cylinder to a full
cylinder. In other words, it would have doubled its volume. Using Boyle's law it may
be calculated that the pressure in the cylinder in this case would therefore be halved
from 100 kPa to 50 kPa. From these calculations it is seen that the partial pressure of
this nitrous oxide is 50 kPa and, similarly, the oxygen pressure is also 50 kPa. So by
applying Boyle's law and Dalton's law, the partial pressure of a gas in a mixture is
obtained by multiplying the total pressure by the fractional concentration of the gas.
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Figure 9: Application of Dalton's law in an Entonox cylinder.
A second example is illustrated by Fig. 10, using a cylinder of air at an ambient
pressure of 100 kPa. The 20.93% oxygen in the air exerts a pressure of 20.93 kPa
and the nitrogen pressure is 79.07 kPa. The calculations can also be made in terms
of millimetres of mercury pressure, remembering that an ambient pressure of 100
kPa represents about 750 mmHg. The oxygen partial pressure works out at 157
mmHg, and nitrogen at 593 mmHg.
Figure 10: Application of Dalton's law in an air cylinder.
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Manufacturers make use of Dalton's law when filling cylinders with gas mixtures.
Figure 11 illustrates the filling of a cylinder to produce a 10% carbon dioxide in
oxygen mixture. The cylinder is first filled with carbon dioxide to an absolute pressure
of 13.8 bar. At this pressure carbon dioxide is still gaseous at room temperature.
Oxygen is then added to a total absolute pressure of 138 bar. The overall percentage
of carbon dioxide is then 10% , the same as the ratio of the pressures.
Figure 11: Dalton's law in the filling of a cylinder of 10% carbon dioxide in oxygen.
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5. AVOGADRO’S HYPOTHESIS
Consider the situation illustrated in Fig. 12. Two syringes each of volume V are
shown containing two different gases, oxygen and hydrogen, maintained at the same
temperature. If the appropriate gas molecules are added to each until the pressure in
the two syringes is the same, it is found that each syringe must contain the same
number of molecules.
Figure 12: Syringes of gas at the same volume, pressure and temperature contain
the same number of molecules
The fact that there are equal numbers of molecules is known as Avogadro’s
hypothesis:
Avogadro's hypothesis states that equal volumes of gases at the same
temperature and pressure contain equal numbers of molecules.
Note that, as the molecular weights of oxygen and hydrogen are different, the
masses of the gases in the syringes must be different. Thus, rather than express a
quantity of gas in terms of mass, it is more convenient to use a concept related to the
number of molecules. This is the mole (Fig. 4.13).
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A mole is the quantity of a substance containing the same number of particles as
there are atoms in 0.012 kg of carbon 12.
It is found that the number of atoms present in 12 g of carbon 12 or the number of
particles, for example, molecules, in one mole of any other substance is 6.022 x 1023,
and this is known as Avogadro's number. It is found that one mole of any gas at
standard temperature and pressure occupies 22.4 litre, and so 2 g of hydrogen or 32
g of oxygen or 44 g of carbon dioxide occupy 22.4 litre at s.t.p. (2, 32 and 44 g are
the respective molecular weights).
As an example of the mole and Avogadro's hypothesis consider the technique of
calibration of a vaporizer illustrated in Fig. 4.14. For convenience, measurements are
given as at s.t.p. On the left of the figure a steady stream of oxygen is shown flowing
into the vaporiser and completely vaporising the 19.7 g halothane into a volume of
224 litre. What would be the mean percentage concentration of halothane? The
molecular weight of halothane is 197, and so 197 g halothane is 1 mol and would
occupy 22.4litres at s.t.p. The 19.7 g halothane in the vaporizer is 0.1 mol and would
occupy 0.1 x 22.4litres or 2.24Iitres. This halothane, however, has been vaporised
into a volume of 224 litres and therefore the concentration of halothane equals 2.24
divided by 224 or 1% .
If measurements were made at temperatures and pressures other than s.t.p., then
the appropriate gas laws would need to be applied and suitable corrections made.
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A very slight error may be introduced because halothane vapour does not obey the
gas laws as closely as a gas such as hydrogen, but the results still provide a good
approximation.
The only satisfactory means of keeping a check on the contents of carbon dioxide,
and nitrous oxide cylinders is by weighing them. The weight of the empty cylinder is
known as the tare weight and is always stamped at the top. Consequently, by
weighing the cylinder the nitrous oxide content may be calculated. An example is
illustrated in Fig. 4.15. A typical full nitrous oxide cylinder contains 3.4 kg of nitrous
oxide. The molecular weight of nitrous oxide is 44 and so one mole is 44 g. If the
measurements are made at s.t.p., what volume of nitrous oxide is obtained from this
cylinder? The calculation is as follows:
1 gram-molecular weight (1 mol) of nitrous oxide is 44g and occupies 22.4 litres at
s.t.p.
Therefore:
3400 g nitrous oxide occupies:
22.4 X
3400
44
litres = 1730litres
The volume of nitrous oxide at s.t.p. is 1730 litres . What is it at15°C?
According to Charles’ law:
V1 V2
=
T1 T2
1730
V2
=
273 273 + 15
V2 =
1730 × 288
= 1825litres
273
The specific volume of gaseous N2O is 22.4/44 = 0.509 litres per gram at s.t.p and
with the same calculation it is at 15°C 0.509 X 288/273 = 0.537 litres per gram
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6. UNIVERSAL GAS CONSTANT
The concept of the perfect gas laws can be combined with that of Avogadro's
hypothesis and the mole as follows:
PV = Cons tan t (k1 )
V
= Cons tan t (k2 )
T
P
= Cons tan t (k3 )
T
Therefore:
P1V1 P2V2
=
T1
T2
PV
= Cons tan t
T
PV = nRT
It is found that PV/T equals a constant for a given quantity of gas and for 1 mole of
any gas PV/T equals a unique constant known as the universal gas constant R. The
more generally applicable equation with slight rearrangement can be written as
PV = nRT , where n is the number of moles of the gas and may be greater or less
than one. This equation has many practical applications.
Example1
This formula is applied in anaesthetic practice in the contents gauge of a gas
cylinder. The gas cylinder has a fixed volume. Therefore, V in the equation is
constant. R is a constant, and if the cylinder is at a fixed temperature, T is constant.
Thus, from the formula, P is directIy proportional to n, the number of moles. The
pressure in the cylinder is therefore directIy proportional to the number of moles in
the cylinder and so to the amount of gas in the cylinder. The pressure gauge thus
acts as a contents gauge provided the cylinder contains a gas.
Example 2
Suppose that the pressure gauge of a 10 l capacity oxygen cylinder indicates a
pressure of 2,000 Ibf /in2 in a laboratory at 20°C, what would be the reading of the
gauge if the cylinder was taken into an operating room at 24°C? Assume that the
volume of the cylinder remains constant. Provided that the units chosen to express
pressure, volume and temperature are the same on both sides of the equation, it
does not matter what these units are.
P × 10
= 2
273 + 24
273 + 20
2OOO × 10
P =
2
2000 × 297
293
= 2028lbf / in
2
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Example 3
By the use of this equation, it is possible to change gas volumes measured under
one set of conditions to those which would obtain under another set of conditions.
This manipulation is often necessary to compare results. It is advocated to quote
b.t.p.s. for the conditions under which lung volumes and ventilation are to be
measured, a. t. p.s. for maximal inspiratory and expiratory flow rates, and s.t.p.d. for
oxygen consumption and carbon dioxide output.
b.t.p.s= body temperature and pressure, saturated
a.t.p.s.= ambient temperature and pressure, saturated
s.t.p.s.= standard temperature and pressure, dry (273 K,101.3 kPa or 760 mmHg)
Suppose that a patient expires into a Douglas bag which is then removed into
a laboratory at 20°C and squeezed out through a dry gas meter. From a knowledge
of the number of expirations collected and the respiratory frequency, the volume of
gas at 20°C corresponding to the minute volume can be calculated easily. If the
minute volume was six litres, what would this volume, which is measured under the
conditions of ambient temperature and pressure, saturated (a.t.p.s.), become when
referred back to the conditions of body temperature and pressure, saturated
(b. t. p.s. ) ?
Assume that the patient's body temperature is 37°C, the saturated vapour pressure
of water is 18 mmHg at 20°C and 47 mmHg at 37°C and that the barometric pressure
is 760 mmHg. In order to work only in terms of gas pressures, the appropriate water
vapour pressures must be subtracted from the barometric pressure (see also later).
(760 − 18) × 6 (760 − 47) × V2
=
273 + 20
273 + 37
V2 =
742 × 6 × 310
= 6.61litres
713 × 293
What would be the volume of the six litres, measured under atmospheric conditions,
when referred to the conditions of standard temperature and pressure, dry (s.t.p.d.)
i.e. 760 mmHg and 0°C?
(760 − 18) × 6 760 × V2
=
273 + 20
273
V2 =
742 × 6 × 273
= 5.45litres
760 × 293
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7. CRITICAL TEMPERATURE
It has been assumed that all gases obey the gas laws perfectly, but in practice slight
deviations occur. Hydrogen obeys the gas laws most closely and for this reason the
hydrogen thermometer is used for measurements in the international temperature
scale. As a gas cools to near its liquid boiling point, its behaviour deviates from the
gas laws.
Figure 16 compares the filling of a nitrous oxide cylinder with that of an oxygen
cylinder at an ambient temperature of 20°C. In the top diagram nitrous oxide is being
pumped under pressure into the cylinder but, once a certain pressure has been
reached, the nitrous oxide liquefies without further increase of pressure until the
cylinder is filled to the appropriate level. In the case of oxygen, however, as it is
pumped into the cylinder, the pressure gauge indicates accurately how full the
cylinder is. No matter how much pressure is applied to the cylinder it is impossible to
turn the oxygen into its liquid form at normal room temperature.
Figure 16 : Filling of a nitrous oxide cylinder, and an oxygen cylinder.
If, instead, the oxygen cylinder were filled at a very low temperature below -119°C,
then it would be possible to liquefy the oxygen. In other words, it is found that there is
a critical temperature for oxygen -119°C above which oxygen cannot be liquefied by
pressure alone. At or below this temperature, liquefaction under pressure is possible.
Each gas has its own critical temperature.
Critical temperature is defined as the temperature above which a substance
cannot be liquefied however much pressure is applied.
The critical pressure is the vapour pressure of the substance at its critical
temperature. The critical temperature of nitrous oxide is 36.5°C. Consequently, the
nitrous oxide in a cylinder is a gas if the temperature is above 36.5°C as might occur
in the tropics.
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Figure 4.17 illustrates a large syringe of nitrous oxide at constant temperature T°C
which is above 36.5°C, and shows graphically the results of compression of the
syringe. The line on the graph traces the pressure increase produced as the volume
is reduced.
A series of such lines of pressure against volume can be produced at
various temperatures and these are known as isotherms.
Figure 4.18 shows the isotherms for nitrous oxide at 40°C, 36.5°C, and
20°C. The top line indicates the changes at 40°C. As the volume is reduced,
moving from right to left on the graph, there is a smooth increase in pressure
according to Boyle's law. The curve produced is a rectangular hyperbola. At the
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critical temperature (36.5°C) there is a critical pressure of 73 bar (1 bar = ± 1 atm) at
which the nitrous oxide liquefies.
One characteristic of a liquid is that it is relatively incompressible and so, when the
gas has completely turned to liquid, the slightest decrease in volume is associated
with a great increase in pressure. An almost vertical line occurs at this point as
shown on the graph. Of greater interest is the bottom isotherm illustrating the results
at a room temperature of 20°C. As the nitrous oxide in the syringe is steadily
compressed, at a pressure of 52 bar some of it liquefies as shown in the lower area
of the graph. At this point, both liquid and vapour are present and any forther
decrease in volume causes more vapour to condense and the pressure to remain
unaltered. Consequently a horizontal line is present on the graph at 52 bar, and this
is the typical pressure in a nitrous oxide cylinder at room temperature, being its
saturated vapour pressure. When all the nitrous oxide vapour is condensed into
liquid, then any attempt to reduce the volume results in the sharp increase of
pressure indicated by the near vertical line in this area of the graph. Note that the
word nitrous oxide gas is used for the upper tracing and nitrous oxide vapour for the
lower tracing. Strictly speaking the word 'gas' applies to a substance above its critical
temperature while 'vapour' is the word used for a substance below its critical
temperature. So at normal room temperature, oxygen and nitrogen are gases
whereas nitrous oxide, carbon dioxide, halothane and ether are vapours.
Consider the hypothetical case of a nitrous oxide cylinder filled completely with liquid
nitrous oxide. Any increase in temperature causes the nitrous oxide to expand but,
unlike a gas, a liquid is not compressible. As a result, there would be a great increase
of pressure and a considerable risk of explosion. To obviate this risk the
manufacturers always ensure that the cylinders are only partially filled in order to
leave a volume of nitrous oxide vapour above the liquid. Any increase in temperature
then causes the liquid to expand, which compresses this vapour and, as the vapour
is compressed, some of it condenses, thereby keeping the pressure from rising
excessively. In practice, nitrous oxide cylinders are filled according to their weight
and for a given size of cylinder there is a fixed quantity of nitrous oxide so that there
is no risk of explosion should the cylinder be over-heated.
The term 'filling ratio' is used to describe how much gas is used to fill a cylinder. The
filling ratio is the mass of gas in a cylinder divided by the mass of water which would
fill the cylinder. As 1 litre water weighs 1 kg the filling ratio represents the mass of
nitrous oxide in kilograms over the internal volume of the cylinder in litres. For nitrous
oxide this ratio is 0.65 in the United Kingdom.
The withdrawal of gas from a nitrous oxide cylinder.
A 'full' nitrous oxide cylinder contains both liquid and gaseous nitrous oxide if the
ambient temperature is below the Critical Temperature of nitrous oxide, 36.5°C . In
hot climates, where the ambient temperature is above 36.5°C, the cylinder will
always contain only gaseous nitrous oxide. At 37°C, the pressure in the cylinder
would be 1.125 lbf/in2 (76.5 atm) and this would fall steadily as gas is withdrawn.
At 20°C, the saturated vapour pressure of nitrous oxide is 51 atmospheres (750 lbf/
in2) , so that this will be the pressure indicated on the cylinder gauge if one is fitted.
When gas is withdrawn at temperatures below 36.5°C, the liquid nitrous oxide boils,
replenishing the gas which has been withdrawn. The heat necessary to produce this
evaporation comes from the atmosphere of the room, and has to be transferred
through the cylinder wall. If the rate of withdrawal is sufficiently high, a frost may form
on the bottom of the cylinder. Expansion of the issuing gas at the cylinder valve may
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cause a marked cooling, and for this reason precautions are taken by the
manufacturer to ensure that the gas is dry. This prevents ice formation from blocking
the valve. In practice it is possible for the issuing gas to have a temperature of -60°C.
The cylinder pressure gauge will indicate a steady pressure of 750 Ibf/in2 as long as
any liquid nitrous oxide remains in the cylinder. Once this has all evaporated, only
gaseous nitrous oxide remains, and the pressure then falls steadily until the cylinder
is empty. This is in contrast to the case of an oxygen cylinder where the cylinder
pressure falls steadily all the time gas is withdrawn. Hence the pressure gauge on a
nitrous oxide cylinder does not provide a reliable indication of the capacity of gas
within the cylinder. The better method is to weigh the cylinder
PSEUDO-CRITICAL TEMPERATURE
The term 'critical temperature' applies to a single gas. When a mixture of gases is
present such as the 'Entonox' mixture of 50% nitrous oxide and 50% oxygen, there is
a specific critical temperature at which the gas mixture may separate out into its
constituents. This is a different concept to the critical temperature of a single gas, and
so the term 'pseudo-critical temperature' is often used for such gas mixtures. In the
case of Entonox cylinders it is found that there is a risk of separation if the
temperature in the cylinder falls below -5.5°C. Such separation is most likely if the
cylinder pressure before cooling is 117 bar and is found to be less likely at higher or
lower pressures. In Entonox in pipelines, for instance, the pseudo-critical temperature
is much lower. It is below -30°C at the pipeline pressure of 4.1 bar. Consequently,
there is normally no risk of separation of the nitrous oxide mixture in pipelines.
THE ABSOLUTE SCALE OF TEMPERATURE
On the Celsius Scale of temperature, the temperature of melting ice is taken as 0°C.
On the Absolute Scale, 0°Absolute is the lowest possible temperature that can ever
be attained, and corresponds to -273°C. The intervals corresponding to a degree are
the same on both Celsius and Absolute Scales. Thus 0°C corresponds to 273° A.
There are no negative temperatures on the Absolute Scale. In order to convert °C to
° A, simply add 273, e.g. 20°C = 293° A. °K is more usually written than °A. It is socalIed after Lord Kelvin who contributed much to the study of heat.
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8. DALTON’s LAW, BAROMETRIC PRESSURE AND WATER VAPOUR
Normal PaO2 is dependent on FIO2 and barometric pressure, as weIl as the patient's
age. Air consists of a mixture of gases containing approximately 21% oxygen, 78%
nitrogen and 1% inert gases, a composition that is unchanged throughout the
breathable atmosphere. At any altitude the fraction of inspired oxygen (FIO2 ) is 0.21.
FIO2 is sometimes written as a percentage, e.g., 21 %.
Barometric pressure is a function of the weight of the atmosphere above the point of
measurement. At sea level the barometric pressure averages 760 mm Hg, i.e., air
pressure at sea level will sustain a closed column of mercury 760 mm high. The
higher the altitude, the less weight of air at that point and the lower the barometric
pressure. At the highest point on earth, the summit of Mt. Everest, barometric
pressure is only 253 mm Hg
Barometric pressure is the sum of the pressures of all the constituent gases. Each
gas exerts its own "partial pressure, which is the same pressure it would exert if no
other gases were present (Dalton’s Law).
The partial pressure of any gas in dry air is the percentage of gas in the air times the
barometric pressure:
P GAS in dry air = percentage of gas x PB
Table 1 lists the major gases in air and their partial pressures in dry air. Note that for
clinical purposes we round off the percentage of oxygen in the air to .21 (21% ); this
is the FIO2 or fraction of inspired oxygen when breathing ambient or "room"air.
(Though there is a tiny amount of CO2 in the atmosphere, for clinical purposes we
assume an inspired PCO2 of zero).
Table 1 shows the composition and partial pressures of dry air at sea level:
Percentage of
gas in air
Nitrogen
Oxygen
Carbon
dioxide
Other gases*
Total
*Mainly argon
Sea level
partial pressure (mm Hg)
78.08
20.95
593.41
159.22
00.03
00.94
.23
7.14
100
760
20
AVA Cambridge 2000, Basic Physics and Measurement: THE GAS LAWS
Why dry air? Air often contains water vapour, which exerts its own partial pressure:
To obtain the partial pressure of any gas such as oxygen or nitrogen, water vapor
pressure must first be substracted from the barometric pressure since it dilutes out all
the dry gases. Depending on the climate, the amount of water vapor in ambient air
varies from zero to fuIly saturated, and the partial pressure of water vapor from zero
to over 50 mm Hg. For example, if ambient air is partIy saturated so that PH20 is 27
mm Hg, then
P GAS = percentage of gas x (PB -27 mm Hg).
Regardless of the PH20 in ambient air, once air is inhaled it becomes fully saturated
in the upper airway; hence all inspired air has a water vapor pressure of 47 mm Hg.
at 37°C (water vapor pressure varies slightly with body temperature but the resulting
changes in dry gas pressure are trivial). For this reason, knowledge of the ambient
air PH20 is not clinicaIly important.
Since the percentage of oxygen is constant throughout the breathable atmosphere,
but the barometric pressure decreases with altitude, the pressure of oxygen must faIl
with altitude (Figure 1-2).
Figure 1-2. Effects of altitude on barometric pressure (PB). The height of the column
of mercury supported by air decreases with increasing altitude due to the fall in PB. In
this figure PO2 is the partial pressure of oxygen in dry air. Since PO2 = 0.21 x PB,
PO2 also decreases with altitude. (Everest 8000m, Denver 1600m).
21
AVA Cambridge 2000, Basic Physics and Measurement: THE GAS LAWS
To maintain acceptable oxygen levels at extreme altitude there are two broad
options: change the environment or adapt physiologicaIly.
The first option involves increasing either the FIO2 or the barometric pressure.
Airplane cabins are pressurized to the pressure existing around 2000 m (PB around
580 mmHg) whenever planes fly higher than this altitude; this pressurization aIlows
FIO2 to be kept at 0.21 (the air outside the plane that is used to pressurize contains
always 21% O2) throughout the flight no matter how high they fly. Pressurization is
of course not feasible out in the open. The drop in PB (from 760 at sea level to 580
mmHg in the pressurised cabin) and thus of PaO2 of the passenger has insignificant
physiological consequences for the healthy person ( decreasing saturation; see
oxyhemoglobin dissociation curve) but it will be more sigificant for a person with mild
COPD although it should pose no clinical problem if his PaO2 at sea level is 75
mmHg. If the cabin depressurises oxygen is delivered via oxygen masks. Mountain
climbers carry portable oxygen to increase their FIO2 at extreme altitudes (e.g.,
above 6600 m)
The second option is physiological adaptation:
Table : physiological data on inhabitants of Peru living at sea level and at an altitude
of 4.450 m. The alveolar PCO2 has fallen as a result of the hyperventilation, and the
reduced value of the alveolar PO2 has resulted in a lower arterial PO2 and oxygen
saturation.
Sea level
4450 m
Mean barometric pressure760 mmHg
446 mmHg
Ambient Po2 (dry)
158 mmHg
94 mmHg
Effective alveolar Po2
96.2 mmHg
46.4 mmHg
Arterial Po2
87.3 mmHg
44.9 mmHg
Arterial 02sat. of Rb.
Arterial O2 content
98.0%
20.7 ml/100ml
79.6%
23.0 ml/100ml
Alveolar PCO2
39.3 mmHg
30.2 mmHg
Arterial PCO2
40.1 mmHg
33.0 mmHg
Ventilation
7.771./min
9.491./min
b.t.p.s.
b.t.p.s.
22
AVA Cambridge 2000, Basic Physics and Measurement: THE GAS LAWS
In the case of humidified gases such as those in the alveoli, the presence of water
vapour must be taken into account when calculating partial pressures. Suppose, for
example, a meter indicates an end-tidal ( alveolar) carbon dioxide concentration of
5.6% measured as a dry gas. Ambient pressure is 101.3 kPa. To find the true
pressure of the alveolar carbon dioxide PACO2 it is not sufficient to multiply the 5.6%
by the ambient pressure as the alveolar gas is fully humiditied. From an ambient
pressure of 101.3 kPa the water vapour pressure of 6.3 kPa must be subtracted
before multiplying
PACO2 = (101.3 − 6.3) x
5.6
kPa = 5.3kPa
100
The alveolar carbon dioxide pressure is 5.3 kPa. If the calculation is made in
millimetres of mercury , the alveolar carbon dioxide pressure is found to be 40
mmHg.
Capnometers do measure barometric pressure and perform themselves the
mathematical conversion from % to pressure (kPa or mmHg). Some earlier apparatus
erroneously forget to substract water vapour pressure from barometric pressure in
the calculation. This conceptual error was caused by the introduction of new
sampling catheter material that effectively removes water vapour before samples
reach the sample cell. This led some manufacturers to assume, incorrectly, that the
47 mmHg factor used to compute PCO2 in patients would no longer be needed.
MAC is the minimum alveolar concentration of an anaesthetic at one atmosphere
that produces immobility in 50% of subjects exposed to a supramaximal noxious
stimulus. In fact MAC refers to the partial pressure of the anaesthetic in the alveolus
and when equilibrium develops also in the arterial blood and the brain. This means
that at an higher altitude we will have to give an higher concentration then at sea
level to realise the same partial pressure of te anaesthetic.
Theoretical example: MAC of halothane at sea level (760 mmHg) is 0.9%; This
means a partial pressure in the alveolus of (760-47) x 0.9= 6.4 mmHg. At 4450 m
(PB= 446 mmHg) with this concentration we obtain a partial pressure for halothane
of only 3.6 mmHg. To achieve a MAC-partial pressure of 6.4 mmHg at 4450 m we
will have to increase the vaporiser setting to 1.6% . Each 1000 m above sea level we
will have to increase with about 0.12 the vaporizer setting to maintain the same
anaesthetic depth.
1 atm = 760 mmHg = 101.325 kPa
1 mmHg = 0.133 kPa
1kPa = 7.5 mmHg
1 lbf/in2 = O.O68 atm = 51.68 mmHg = 6.87 kPa
1 bar = 100 kPa = 750 mmHg (1 bar = ± 1 atm)
23
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Associationof Veterinarv Anaesthetists
PHYSICSFOR THE ANAESTHETIST
Robinson College, Cambridge, March 26th2000
09.00 - 9.I5:
Introduction
09.15-10.00: Gaslaws: Part 1.
Yves Moens
10.00 -10.45: Exponentialfunction and time constants.
Michael Dixon
10.45-11.15: - Coffee11.15-12.00: Gasvolume andflow measurement.
Simon Young
12.40-12.45: Measuringprinciplesfor analysisof gasesand vapours:Part 1
PeterGootjes
12.45-I4.W: - Lunch -
,
.1.0O-14.45: Gaslaws Part 2.
Yves Moens
1.45-15.30: Principlesof pressuremeasurement.
Michael Dixon
5.30-16.00 - Tea <.00-16.45: Measuringprinciplesfor analysisof gasesand vapours:Paft2.
PeterGootjes
:15 -17.30: Blood flow and cardiacoutputmeasurement.
Simon young
Sponsoredby Matrx
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Exponential Processesand Time Constants
What is an exponential process?
. . . .. .It is a particularsort ofnon linear process.
And just remind me...what is a linear process?
. . . .. .A linear processis one where the quantity changesat the samerate throughout the process.
.
Filling a bath (assuming vertical sides) is a good example ofa linear process:a gaph of water depth against
time is a straight line, assuming that the flowrate fiom the tap is constant.
So what is a non linear process?
.....Anonlinearprocessis one where the rate ofthe processchangesduring that process.A graph ofthe
quantity against time is a curve ratherthan a straight line.
And an exponential is?
..... A particular sort of non-linear process where the rate of change of the quantity is proportional to the
quantity at that time. Think about emptying the bath we just filled. Pull the plug out and assumethat the water
runs straight out onto the floor. The initial flowrate is determinedby the pressurefrom the head of water in the
bath, pgh and the resistanceof the plughole and outlet pipe. As soon as the bath starts to empty, the head of
waterdecreasesandso the flowrate decreases.When the bath is nearly empty, there is very little head of water
and hence a very low flowrate.
Why is this important?
.......It's important to us becausemany of the processesin anaesthesiaare exponential.Understandingthe
processaad why it happensgives us a befter feel for controlling anaesthesia.The key points, compared with a
linear processare:
1.
2.
3.
The majority ofthe changetakesplacevery quickly.
In theory the process never reachescompletion (although for practical purposes, approdmations can be
made).
For a linear process,the overall rate may be quantified in terms of the gradient ofthe graph. (We all did it at
school....increasein Y divided by increasein X). For an exponential process,the overall rate is expressed
in terms ofthe time constant.
And the time constant is?
. . ..The time constant is the time to completion of the process if the initial rate of the reaction were to be
maintained. So it's the time forthe bath to empty if the initial head ofwater were to be maintained. In a pafect
exponential process,the measuredquantity has fallen to 37%oof its initial value after I time constant. After 2
time constants it has fallen to 13.50Äand after3 time constants, 5o/o.For practical purposes, an exponential
processis usually taken to be complete after3 time constants.
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So how different is it from a linear process?
......If we taketheequivalentlinearprocess
asonethatis completeafter3 time constants,
and discountthe last
SoÄ,thenafterl time constant,the linear processhas only changedto 68yoof its initial value, comparedwith
37o/ofor the exponential.
Where are the exponentialprocesses
in anaesthesia?
........A goodfustexampleis thetakeupof anaesthetic
vapourinto the bloodstream.
Assumefor a momentthat
we havea rebreathingcircuit with a constantconcentration
vapour, so the lungs see the same
of anaesthetic
concentration
with eachbreath.Initially, thereis no anaesthetic
in the bloodstream,so the "gradient"acrossthe
lung wall is high (a bit like the high headof waterin the bath when you startto empty it), and so the rateof
transferofanaesthetic
is high. Butas soon as someanaesthetic
has beentakenup, the gradientacrossthe lung
wall reducesand so, therefore,does the rate of trarsfer. So, for these conditions, a graph of anaesthetic
concentration
in the bloodstreamversustime would be an exponentialcurve.
Real anaesthesia
is more complicatedbecausethe blood is recirculating,and becausethe anaesthetic
is also
beingdissolvedout into the tissuesof the organs.Therearealso time constantsassociated
with the breathing
circuit.
Note also that stepchangeswithin an exponentialprocessare also exponentialtassumethat equilibrium has
beenreachedin the exampleabove.Ifthe concentration
in the breathingcircuit is changed,
ofthe anaesthetic
thenthe takeupinto the bloodstream
will be o(ponentialagainto the new equilibrium level, but with the same
time constantasfor the first change.
And is transferinto the tissuesexponentialas well?
........Yes.The sameprincipleofagradientaoossthetissueappliesbut the anaesthetic
hasdifferenrt
solubility
in eachorga4 which meansthat they take up anaestheticat differentrates.....Sothe processis a set of
exponentialcurves,eachwith its own differenttime constant
Doeswashoutwork the sameway?
.....Yes it does.A simple exampleis the nitrogenwashoutcurvewherethe patientis breathingoxygen
througha non-rebreathing
valve. Analysisof the expiredgas shows exponentialreductionof nitrogen in the
lungs, falling froman initial concentration
of 79/oto, ideally, lessthan2.50Äin 7 minutesfor a human.
Returningto our bathanalogy,imaginethat the bathis fult andthat the wateris muddy. Thentakethe plug out
andturn the tap on so that the levelofwaterstaysconstant.Assumeperfectmixing (put the tap at the otherend
of thebathto theplug),andthemuddyness
will initially rcducequitequickly.....butit will takea long time to
clearthe watercompletely.
Anotherexampleis washinga stainout of your clothes....the
staininitially becomes
fainter,and it all looks
hopeful,but it takesa very very long time to shiftthe last bit.
z
A more complicated example is the concentrationofanaestheticin the blood during washout becauseit will be a
combination ofthe individual exponentialcurves for all the organs. This is known as a multiple exponential and
there are graphical and mathematical methods for separatingthe time constantsofthe components.
How about breething...is that exponential?
.......There is an exponentialelementto it, but spontaneousbreathing is complicated by the feedback
mechanismsin the diaphragm.
Expiration during ventilation is largely exponential: The tissues ofthe lungs are stretchedelastically as the lung
is filled. When expiration starts, there is a high pressuredifferential between the lung and the outside world. If
quiet respiration is assumed, the expiratory flow is mainly laminar, and the flowrate is proportional to this
pressuredifferential.When gas flows out of the lung, the volume decreasesas the tissues rela:<elastically. The
pressurein the lung reducesand the flowrate hencedecreases.
The time constant of the processwill be atrectedby the elasticity of the lung. This elasticity is normally
describedas compliance.
And compliance is?
For a one dimensional linear spring, compliance is defined as the deflection/load. So a high compliance spring
is a soft one which gives a large deflectionfor a given load. Compliance is the reciprocalof stiftress.
Lung tissue may be thought of as a tkee dimensional spring, where linear deflection has been replaced by
volume change,and forcehas beenreplacedby pressure(forcdarea).Note that the units remain consistent.
A low compliance lung is one wherethe tissues areunusually stif and a high compliance lung is one where the
tissues are floppy.
So for a lung, a change in conrpliance rezults in a change in tidal volume for an applied pressure. I-ow
compliance results in low tidal volume becausethe spring is stiff Expiration also ocqrs quicker.
The lung also has a resistanceto flow, in the same way that nuurowtubes have a higher resistancethan wide
tubes. Assuming laminar flow, the relationship baween the pressuredifferentialand the flowrate is linear.
Typical values for a human are:
Compliance0.5 litre kPa''
Resistance0.6 kPa s [itre-'
The time constant Tc is the product ofthese two parameters.
A low compliancegives a short time constant becausethe spring is stiffer.
A low resistancegives a short time constant because the volume flowrate is higher for a given pressure
differential.
Time Constants in Anaesthetic Breathing Circuits
The vaporizer
The oxygen supply is initially from a cylinder at high pressure,regulated to 60 psi at the cylinder, and then
down again to a more convenient pressurewithin the anaestheticmachine. The flowrate into the breathing circuit
is then controlled.
A proportion ofthe oxygen flow through the vaporizerinto the circuit is diverted to the vaporisation chamberby
a bypassvalve Modern vaporizersare designed so that the flow leaving the chamber is saturated.The takeup of
vapour into the oxygen flow is thus not exponential when measuredat the outlet ofthe chamber.
Note that there may be a non linear element to some older vaporizerswithout thermal control: the latent heat of
vapourisation causesthe temperatureofthe vaporizerto drop and thus the saturatedvapour pressurereduces,
3
The rebreathing circuit
The volume flowrate of anaestheticgas into the circuit can be varied by changing the orygen flowrate, or by
adjustment of the bypass valve to vary the flow through the vapourisation chamber and tMore
change the
concentrationof vapour leaving the vaporizer.
The mixing ofthis vapour into the rebreathingcircuit is an exponential process,with a time constant controlled
by the flowrate (he higher the flowrate, the shorterthe time constant).
At the start ofanaesthesia,a high flowrate is set with the popofvalve open. This gives a high concentrationof
anaesthetic, aiding rapid induction of anaesthesiain the patient and a short time constant ör the nitrogen
washout.
An awarenessofpollution, combined with the high cost ofmodern inhalable anaesthetics(such as isoflurane) has
led to widespreadadoption oflow flowrates during the operation. This results in longer time constantsand more
time to react.....buta slower r€spons€.
The first reactionifdeeper anaesthesiais requiredis often to adjust the vaporizerto give a higher concentrationof
anaesthetic into the circuit. This is necessaryif equilibrium has been reached,but quicker results will be
achievedby simultaneously increasingthe flowrate, reducing the time constantin the circuit.
Ofteqhowwer,takeupis onthelong tail of the exponentialcurve (somewhereafterthe secondtime constant),
and increasingthe flowrate alone may be suffcient
page1
Physicsand Measurementin Anaesthesia:Gas volumes,
gasflow, blood flow and cardiac output
Gas volumemeasurement
Spirometry
Spirometersdirectly measurethe volumeof gasfrom first principles.The water
spirometeris consideredthe goldstandardfor volumemeasurement.
They arebulky,
havea slow responseandareusedfor researchratherthan clinicalwork.
Water spirometer
The waterspirometerusesa metalbell suspended
in a waterseal.The bell is
gas
counterweighted
so that the
The cross-sectional
insideis at ahospheric pressure.
areaof the bell is constantso thatif gasis addedto or removedfrom the bell it movesup
or down by an amountproportionalto the volume.The verticalmovementof the bell is
of the gasinsidethe
measureddirectly with a ruler, or electronically.The temperature
bell is measuredso thatthe gasvolumecanbe correctedto STPDor BTPS.Larger
spirometersalsohavea fan insideto makesurethe gascompositionis uniformand
isothermal.
CO, atrsorber
A wet spirometer.Kymographdrumsareobsoleteand the outputwould normallybe
electronicusinga rotationalsensorattachedto oneof thepulleys.
Page2
Dry spirometer
Dry spirometers
do not usewaterto providethe gassealandaremorepracticalfor
clinical work. One typeusesa low friction rolling diaphragmto sealthe piston.Other
typesusefoldedbellows.Movementof the pistonor bellowsis detectedelectronically.
were extensivelyusedfor pulmonaryfunctiontestingbut arebeing
Dry spirometers
replacedby pheumotachograph-based
systems.
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Dry spirometers,rolling diaphragm and bellows type.
Wright's respirometer
The Wright's respirometerhas a set of lightweight vaneswhich rotateas air passesover
them. The rotation of the vanesis measuredeither mechanically or electronically. In the
mechanical system the rotation of the vanesis connectedvia gearsto a dial indicator. In
the electronic version the rotation is measuredoptically. Wright's respirometersare oot
as accurateas spirometersbut are much more convenientto use.
Wright's respirometersare used extensively in clinical practice to measuretidal volume
in anaesthetisedpatients.They come with standard22mrn connectorsand can be inserted
into a circle system or attachedto the endotrachealtube.
. 0blrcile
chänFd.,is t?
clrr.tcl arr Hr-.w
Cross-sectionof a Wright's respirometer.
page3
A Wrights spirometerfor clinical use.
Body plethysmography
The person or an animal is placed in a sealedbox but breathesair from outside the box.
This can either be done via a tube or by using a "head out'' box with a neck seal.As the
subject breathesin, the chest wall moves out and displacesa volume of air equal to that
inhaled. The displacedair is measuredin one of two ways.
1) The box is sealed,so that the pressurerises as the subjectin-hales(a constantvolume
plethysmograph).The rise in pressureis measured,and the volume is calculatedfrom the
gas equations.
2)Tlne box is open to the atmospherevia a pneumotachograph(constantpressurebox).
As the subjectinhales an equal volume of air is displacedfrom the box. This volume is
measuredusing the pneumotachograph.
Corrections are neededto the gasvolume becausethe inhaled room air is warmed and
humidified by the respiratory system and therefore expands.The expansionfactor
dependsupon the temperatureand relative humidity of the room air but is typically
around lÜVo.The body plethysmographis a useful device becauseit can be used to
measurelung mechanicsand functional residual capacity as well as tidal volume. It is
extensively usedin the measurementof respiration and lung function in laboratory
rodents.
The sameprinciple is sometimesused to measurethe tidal volume of animals on a circle
system.The reservoir bag is placed inside a constantpressureplethysmograph(the "bag
in a box" system).The tidal volume is measureddirectly using the pneumotachographin
the side of the box. This avoids having to place the pneumotachographdirectly in the
circuit.
Precision syringe
and
Precision syringesare used as primary stendardsto calibrate pneumocachographs
spirometers.They are available in a wide range of sizesfrom 10ml to severallitres.
page 4
Integrationof flow
The mostcommonmethodof measuringrespiratorygasvolumeis by integratinggas
The volumeis theintegralof the
flow. Gasflow is measuredusinga pneumotachograph.
flow:
volume=/flow. dt
The gas flow is converted !o an electrical signal by the pneumotachograph.The flow
signal is then integrated electronically. Analogue integrators were usedfor many years
but digital systemshave taken over. Drift, causedby small offsets in the flow signal, is a
major problem with the integration technique. It is solved by resening the integrator after
every breath.
are used 8omeasuretidal volume and respiratory rate in ventilators,
Penumoüachographs
pulmonary function testing systemsand anaestheticmonitors such as the Datex.
Gas flow measurement
Physicsof fluid flow in tubes
Fluid flow in a long tube at low flow ratesfollows the Hagen-Poiseuillelaw.
flow =.4'
Srtl
where r = tube radius, p - pressuredrop acrossthe tube, I = tube length and Tl - viscosity.
Note the strong dependenceof flow on tube radius. Also, flow rate is independentof gas
density and dependsonly on the gasviscosity.
Flow under theseconditions is said to be laminar. For a given tube size and fluid, flow is
proportional to pressureand vice versa.The flow profile, i.e. the velocity of the fluid
acrossthe tube, is parabolic.
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As flow rate increasesthe flow pattern changesfrom laminar to turbulent. Turbulent flow
is very complex to model. An empirical description is:
page5
flow = kpn
where k dependsupon the tube dimensionsand gas properties.n varies between I and2.
For a given flow rate, turbulent flow requiresa greaterpressuregradient than laminar
flow. The flow profile is also no longer parabolic and tends to be flatter, i.e. the flow is
more constantacrossthe tube.
In small airways, veins and peripheral arteriesthe flow is laminar. In the aorta and large
airways flow is turbulent. Turbulent flow producesaudible vibrations and is the origin of
most breath sounds.It also producesthe Korotkoff soundsthat are used to measureblood
pressureclinically in humans.
The type of flow pattern presenthas great importance in the measurementof air and
blood flow. Several methodsfor measuringflow actually measurevelocity, for example
Doppler systems.The flow is estimatedby measuringthe diarneterof the vesseland
assuminga laminar or turbulent flow profile.
The type of flow presentcan be estimatedby the Reynolds number.
Nr =
2ilP
rl
where Nr is the Reynoldsnumber,r is the tube radius,v is the averageflow velocity, p is
the fluid density and I the viscosity. The transition betweenlaminar and turbulent flow
occurs at a Reynolds number of about ?l0f,.. However, the flow pattern is greatly
influenced by bends and branchesin the tube and by surfaceroughness.
A tube has to be about ten diametersor more in length and sraight for a fully laminar
flow pattern to develop. Tubes that are shorterthan tlis, or which have frequent branches,
bendsor changesin diarneter,cannot supportfully lamiaar flow.
Rotameter
The rotameteris widely usedto measuregasflow in pipes. It can only measuresteady
flow in one direction, and has to be calibratedfor a specific gas.Rotametersare relatively
cheapand reasonablyaccurate(2Vofor the bestrotameters,SVotypical).
A rotameterconsistsof a light metal bobbin inside a taperedtube. Gas flowing up the
tube supportsthe weight of the bobbin. As the gasflow increases,the bobbin moves up to
where the tube is wider. The bobbin spins in the gasflow to increasestability and prevent
the bobbin from touching the walls of the tube. Cheap rotatmetersuse a glassor metal
ball as a float.
Rotametersare universally usedto measurefresh gasflow on anaestheticmachines.
page6
Pitot tube
A tubefacinginto the flow of a gasexperienggs
a higherpressurethanoneat right angles
to the flow. This differenceis causeduy the kinetic
of theflowing gasbeing
"ortö
convertedto potentialenergy.The Pitot tubeusesthis
efiäct to measuregasvelocity.A
sensortubefacesinto the gasflow andmeasures
the dynamicpressure.
Ä secondtube
measures
the staticpressureat the samepoint. The difieren", ir, pressureis relatedto
the
gasvelocity.
velocity= klffiwhere k is a constant for a given gas and tube size. The total flow
is calculatedby
assuminga flow profile. The errors in this assumption,plus the
nonJinear nature of the
sensor,make it unpopular for clinical use. However, the "D-lite"
sensorused with Datex
anaestheticmonitors appearsto work on the pitot tube principle.
The Datex uD -lita" pneumotachograph.
Pneumotachographs
Pneumotachographsare extensively used to measureairflow in
clinical applications.A
pneumotachographis a tube that contains a small resistanceto
airflow. Over a certain
range of flows the resistanceis constantso that the pressuredrop
acrossthe resistor is
proportional to the flow. The presstuedrop is measuredwith
a sensitivepressure
transducer.Pneumotachographsare bidirectional, have a rapid response
and are the
sensorof choice for measuringrespiratory airflow.
Pneumotachographsrely on the viscosity of the gas to generate pressure
a
gradient, and
thus they are affected by changesin gas viscosit!. Thei should
be calibratedwith the
samegas mixture that they are used to measure.This ii not always
easyand the error is
often ignored in clinical practice. Pneumotachographsare usually
calibratedwith dry air
at room temperature.Inside an anaestheticcircuit they will be
filied with moist oxygen at
an elevatedtemperature.One way around this probleä i, to use
a bag-in-a-box system.
Pneumoüachographs
usedfor clinical applications are often heatedto prevent
condensationof water vapour, which greafly affects their calibration.
pageT
Fleisch
The Fleisch pneumotachographhas a resistive element made up from a bundle of long,
thin metal tubesin parallel. The aim is to produce laminar flow in the tubes.Under thäse
conditions the pressureacrossthe resistor is proportional to the flow, from the HagenPoiseuille law. Fleisch pneumotachographsare usually heatedbecauseof their large
mass.They are accuratebut expensive.
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Screen tl.illg
Screenpneumoüachographs
use a fine stainlesssteel mesh as the resistive element.They
are lightweight, cheaperthan Fleisch pneumotachographsand have a better high
frequency response.They can be heatedbut often are not becausethe thin mesh heatsup
rapidly to the temperatureof the airflow.
Tp drtlürerlttill frrnäsurö
lron!idrfgef
,.*'i.*-'"
,/**
Go,rro
Screenpneumotachograph.
Ultrasonic
The ultrasonic pneumotachographusesthe speedof sound in the gas to measureits
velocity. A pulse of ultrasound is sent acrossthe tube in one direction and the transit time
is measured.A pulse is then sent in the opposite direction and the time measuredagain.
The difference in transit time is proportional to the airflow. The apparentdifference in the
speedof sound in the gas in the two directions is causedby the movement of the gas,
which carries the sound wave. Although the apparentspeedof soundin the gas is
proportional to its velocity, the pneumotachographmeasuresflow. This is becausethe
ultrasound travels acrossthe entire airflow and its speedat any point is affected by the
gasflow at that point.
Ultrasonic pneumotachographshave very little resistanceto airflow since they are
effectively empty tubes.They are usedin exercisephysiology becausethey do not
page8
interfere with the high respiratory airflow generatedat maximal exercise.The speedof
sound in a gas is affected by its density and thus ultrasonic pneumotachographsare
sensitiveto gascomposition.
Fleceivor2
Trenvnrtfnr t -< /
Ftow -
t
)r''ftarßmifla(
2
Ultrasonic pneumotachograph.
Rotating vane
Rotating vane pneumotachographsare very similar to Wright's respirometerswith an
optical sensor.They are not usedmuch becausethey are delicate and their inertia leads to
measurementerrors.
Cal ibration of p neumotachoI raphs
Pneumotachographshave to be calibrated before use. One way is to passa known flow
rate of gas(from a precision rotameter)through the pneumotachograph.However, the
usual way to calibrate pneumotachographsis with a precision syringe. Rememberthat
volume is the integral of flow. If the calibration factor of the pneumotachographis k,
then:
volume = k/flow.
dt
This re-arrangesto give:
k=
volume
/flow.
dt
Since the volume is known. k can be calculated.
Gasvolumeandflow correction
It is very importantin researchwork that gasvolumesarecorrectedto specified
conditions.Volumesaremeasured
underthe conditionspresentin the laboratory(ATP,
pressure).
actualtemperature
and
The two standardconditionsareSTPD(standard
andpressure,saturated).
temperature
andpressure,dry) andBTPS(body temperature
STPD
Conditions are 0"C,760 mmHg atmosphericpressure,dry. The conversion to STPD from
ATP is:
page9
Vnpo= Vo* x +"
273+T
P":&7ffi
where T = actual temperature(oC), ps=barometricpressure(mmHg), p"ro partial
pressureof water vapour in the measuredgas.
BTPS
Conditionsarebody temperarure,
ambientpressure,saturatedwith watervapour.The
conversionto BTPSfrom ATp is:
=v^rrx
vsrps
#X"
P, - P"ro
P" - P"ro @Tu"oy
where T = temperafure(oc), Ps=baromehicpressure(mmHg), p'zo = partial
pressureof
water vapour in the measuredgas, pruo @Tr.av= saturatedvapour presiure
of water at
body temperature.
Blood flow
Peripheralblood flow msasurementis usedclinically to assessorgan viability,
and in
researchwork' Cardiac outPut is more frequently mÄasured.It is
in overall indicator of
cardiacfunction and is also usedin the calculatiänofderived functions
suchas peripheral
resistence.
Ultrasonic transit time
Essentially the sami as the ultrasonic pneumotachograph.The method is invasive
becausethe ultrasonic transducersmust be placed riouoO the blood vessel.
The output is
in real time and the method is extensivelyusedin research.
Limb plethysmography
A cuff is placed around the limb. The cuff is inflated to a pressureslightly below
diastolic. This occludes all venousflow but allows arteriai blood to flow
into the limb.
The limb swells with the increasedblood volume and the swelling is measured
using
mercury-in-rubber extensometers.The method is limited to researchapplications
in
humans.
Doppler ultrasound
The velocity of blood in a vesselcan be measurednon-invasivelyusing ultrasound.
A
beam of ultrasoundis fired at the vessel.The frequency of the rehecteä signal
is shifted
* amountproportionalto the velocity of the blood flowing through thJ vessel.
If the
!I
diameter of the vessel is known, and the flow profile, the blood flow can be
calculated.
Also, the angleof incidenceof the beamrelativeto the flow needsto be known.
I
page 10
In practice, the restrictions and assumptionsof the method make it difficult to use
clinically. The diameter of the vessel can be measuredusing the sameultrasound system
in imaging mode. The angleof incidenceusually has to be estimated.The flow profile
also has to be estimatedand is usually assumedto be flat (turbulent). Flow can only be
measuredin arteries, where the Doppler shift is large enough to measure.The subject
must keep still during the measurement.
Cardiac output
Cardiacoutputis a muchmoreusefulmeasurement
thanperipheralbloodflow. Heart
raüe,blood pressureandcardiacoutputarethe key parameters
thatdefinethe stateof the
cardiovascular
system.
Principle of indicator dilution
whose
Blood flows througha pipe.At onepoint an indicator,an inert substance
concentration
in blood caneasilybe measured,is injectediuto theflow. The flow rateof
theindicatoris negligiblecomparedto themain flow. The indicatormixescompletely
with theflow, and at somelaterpoint its concentrationis measured.
flow
--->
'l t
inject indicator
t
measureindicator
F.
In this system,C, = * whereCi = cotrcentration
of indicatoraftermixing (mg/litre,for
F,
example),Fi = räte of additionof indicator(mg/minute,for example)andFo= main blood
flow rate(litres/minute).
Thus F, = +.
Li
For cardiac output measurementsthe indicator needsto be addedto a vessel that takes all
the blood flow to the heart.The indicator can be measuredafter mixing at any convenient
point downstream as long as its concentrationdoes not changeduring its passagethrough
the arterial tree.
The indicator dilution principle can be extendedto include non-constantindicator
injection. In particular, this includes a bolus injection of indicator. As before, the
following assumptionsapply:
1) Flow rate is constanL
2) The volume of indicatorinjected is negligible comparedto the cardiacoutput.
3) The indicator is inert.
page11
A bolus of indicator is injected and the concentrationof indicator is measured
continuously downstream. Measurementis continued until all the indicator has passedthe
sensor,i.e. the indicator concentrationhasreturnedto its pre-injectionlevel. If the flow
rate is Fo and the concentrationis measuredfor time t, then the total volume V that has
flowed in this time is V = Fo .t. The time period t coversthe entireperiod when
indicator was presentin the main flow. Therefore, volume V containsall of the indicator.
If a mass m of indicator was injected, then { ' V= i! where {
ir tn" average
concentrationof indicator in the volume V. Combining this with the earlier expressionfor
V we come up with E = +.
We now needto find Q. The concentrationof indicator
" t, t'
is not constantwith time after a bolus injection.However, we can obtain the equivalent
value by finding the area under the concentration-timecurve. If A is the area under the
(where C, is the instantaneous
concentration-timecurve, then A =
IC,.dt
concentration).But we can obtain the sameareaby replacing the time-varying
concentrationwith the meanvalue f , becauseA = Ei . t. Substituting,we end up with
the equationfor indicator dilution using a bolus injection:
Fo=T-LfC, ' dt
J
0
The time periodt over which theindicatorconcenu?tionis measuredmustincludethe
completeinjection,i,e, startmeasuringbeforethe injectionandcontinueuntil thelevel
falls to the pre-injectionvalue.t can beanyarbitrarytime but thelongerit is the less
accuratethe reading.Also, flow mustbe constantduringtime t.
The following graphshowsan indicatordilution experiment.In this casethe indicator
wasa dye,indocyaninegreen.The areasunderthemain peakandthe rectanglearethe
is 1,39mg.Lt.
same.The meanconcentration
page12
(t,
E
C
.9
curye
actualconcentration-time
2.5
E
C
o
c
()
(J
(J
{)
ä.'
q,
1.5
<-
concentration
average
1
E
(l)
E
C
0.5
ö
(l)
E
0
-0.5
10
20
30
40
50
60
time(s)
There are severalpractical problems that crop up when using indicator dilution
experiments.One is recirculation. If the indicator is not completely clearedin the
peripheral circulation (e.g. indocyanine green and lithium) it will come back round and
be measuredagain. This is clearly visible in tlis dye dilution experiment.The dye
concentrationdoes not go back to baseline,but reachesa minimum at point A and then
startsto rise again as the dye recirculates.It is important to eliminate the effects of
recirculation. Even if the indicator doesnot recirculate (e.g. thermodilution) the curve
often does not reach the baselineagain. We thereforehave to extrapolatethe tail of the
curye back down to baselinebefore calculating the area.
Page13
=
Ct)
E
c
,o
2.5
tr
C
(l)
(J
c
ö
(J
1.5
o
ä
1
E
(l)
a
C
0.5
{)
(I)
T'
0
-0.5
0
10
20
30
time(s)
40
s0
60
The extrapolation is performed by assumingthat the later part of the washout-sectionis
exponential.The time consrantof the exponential section is calculatedand used to extend
the curve back down to baseline.The calculation used to be performed by plotting the
curve on logJinear axeswhich makesthe exponentialsectiona straightline, which could
then be extendedby hand. With cheapcomputing power it is much easierto fit an
exponential function directly to the curye. The next graph shows the result of
extrapolating the curve to baseline.
page 14
=
O)
E
C
.o
E
E
<l)
I
c 1.5
o
()
o
ä
15
(t)
c
C
1
curveextrapolated
to baseline
to removerecirculation
etfect
0.5
{)
L
a(l)
0
rc
-0.5
10
20
30
time(s)
40
50
60
Now the area under the curve (22.23 mg.L-t.s) can be calculated.The amount of dye
injected was 10mg so the cardiac output is calculatedfrom:
cardiac output (litres/minute) -
amount of dye (mg) x 60
areaunderconcentration-timecurye (mg.l-1.s)
giving.a value of ?i7.0L.min-r for this horse.The factor of 60 convertsfrom L.s't
to
L.min-t.
Fick
The indicator in the Fick method is oxygen. Oxygen is addedto the venous blood at a
steadyrate as it passesthrgugh the lun!. The amJunt of oxygen in the blood entering
and
leaving the lung (in the pulmonary artery and a peripheral artery,respectively)is
measured.The oxygen consumption of the animal is also measured.The cardiac output
is
given by:
vo'=
Q= =
Cao - Cvo,
where Q = cardiacoutput (L.min-t), Voz= oxygen consumption(ml.min-r),C,ozand
C,o,
= arterial and mixed venous oxygen contents(ml.Lt).
The oxygen contentsare measuredin the blood samplesusing a blood gasanalyser
along
with a measurementof haemoglobin.Oxygen consumptionis measur"äUy coliecting
page 15
expiredair and measuringits volume and oxygen concentration.The patientmust be in a
steadystate so that oxygen storesare neitler increasing nor decreasing.The method is
inaccurateif large extrapulmonary right-to-left shuntsare present.
The Fick method can also be used with carbon dioxide as the indicator. However,
becauseof the large carbondioxide storesin the body it takesa long time (1130 min) for
the subject to reach a steady state.
Dye dilution
An indicator that was commonly usedis indocyanine green.The concentrationof this dye
can be measuredphotometrically in arterial blood. To perform a measurement,a bolus of
dye of known amount is injected into the right atrium or jugular vein. The concentration
in a peripheral artery is measuredcontinuously by withdrawing arterial blood at a steady
rate through a spectophotometer.Seethe example above for details.The method is not
usedmuch now that thermodilution cathetersare available.
Thermodilution
The most widely used method for measuringcardiac output is thermodilution. Heat is the
indicator. A bolus of cold fluid is injected into the right auium. The fluid mixes with the
blood in the right side of the heart and the temperatureis measuredin the pulmonary
artery. SpecialisedSwan-Ganzcathetersare used for the measurement.The catbeter is
fed down thejugular vein, through the right side of the heart and into the pulmonary
artery.The correct placementis verified by measuringthe arterial pressurefrom a port at
the tip of the catheter.A thermistor at the tip of the cathetermeasuresthe temperatureof
the blood in the pulmonary artery. A bolus of cold dextroseis injected through another
lumen into the right.atrium and the temperahrrein the pulmonary afirlry is measured.The
cardiac output is calculated using the equationabove, with correctionsfor the specific
heat capacitiesof blood and dextrosesolution. The calculationsare perforrred
immediately by a dedicatedcomputer.
I
For small animals and humansa bolus of 2-5ml of room temperaturefluid is sufficient.
For larger animals the injectate has to be cooled to obtain a reasonabletemperaturedrop
in the pulmonary arterial blood. Typically, measurementsin horsesrequire the injection
of 60ml of ice-cold dextrosein less than 5 seconds.
Li dilution
A new methodusesa lithium ion sensitivecatheter.The catheteris placedin a peripheral
artery and monitors the lithium concentrationcontinuously. A bolus of lithium cNoride is
injected into the jugular vein. The method avoids having to place a catheterin the
pulmonary artery, which is the major drawback to the thernodilution method. Uthium is
cleared slowly from the body and so there is a maximum number of measurementsthat
can be made at one time.
page 16
Doppler ultrasound
This is the sameprinciple used to measureblood flow in peripheral arteries.If the blood
flow is measuredin the aorta it will equal the cardiac output (with a small error for the
coronary circulation). The problernsare measuring the aortic diameter and the angle of
incidence of the beam. The flow profile is assumedto be flat (turbulent) in the aorta. The
blood flow in the aorta is pulsatile and reversesat the end of systole as the aortic valves
close. The calculations are therefore performed on a beat-to-beatbasis with corrections
for the negativeflow.
Sternal notch
In humansthe ascendingaorta can be insonated using a probe in tle sternal notch. The
angle of the beam is in line with the flow and the flow profile is flat The aortic diameter
is estimatedusing the patient'sheight, weight, sex etc.
Transoesophageal
In animals the sternal notch approachdoes not work becauseof the differences in chest
anatomy from humans.The descendingaorta can be reachedfrom a probe placed in the
oesophagus.The aorta and oesophagusare assumedto be parallel and the angle of
incidence is the angle at which the transmitter is placed in the probe. The diameter of the
aorüahas to be estimatedfrom nomogramsor by imaging the aorta using radiography or
ultrasound.The method is only suitable for animals that will acceptan oesophagealprobe
and is usually perforrred under anaesthesia.
Cardiac innaging
The stroke volume, an[ thus the cardiac output, can be measuredusing imaging
ultrasound.The stroke volume can be estimatedfrom measurementsof the ventricular
volumes in systole and diastole.Alternatively, the diameter of the oudlow tract can be
measuredand the velocity of the blood found using the ultrasound in Doppler mode.
Bioimpedance
The electrical impedanceof the chest can be measuredusing a small current at a high
frequency (5 - 50 kHz). The impedanceof the chest (Zo) varies stightly during the
cardiac cycle. This variation is assumedto be due to the ejection of blood, which has high
conductivity, into the lungs (which have low conductivity) during systole.The exact
origin of the variation in impedanceis not certain. However, the derivative of the
impedance(dzJdt) can be used to estimatestroke volume and hencecardiac output.
The systemhas limited use.Its great advantageis that it is non-invasive and only requires
the placementof ECG electrodeson the patient. Its accuracyis questionable,especially if
there are changesin body position and it is generally used to track changesin cardiac
output rather than absolutevalues. The non-invasive nature makes it useful in aerospace
applications.It has beenvalidatedin dogs.
"First recordednnasurenrent
of arterialbloodpressure.
Rev.William Harvey,I'l* century".
lntroduction
Gasmeasurementin veterinary anaesthesiapractice is of great importance.A human related
study showedthat nearly 600Äof citical incidents during anaesthesiainvolved either the
patients respiratory system, or the gas delivery systemof the anaesthesiamachine.
Reliable and easyto use monitors of respiratory and anaestheticgas concentrationscan
contribute to patient safety and are now available.
In veterinary practice COz measurement,the capnography, was introduced at the beginning of
the seventies,later on this measurementwas combinedin one multigas monitor with the
measurementof oxygen, nitrous oxide (NzO) and volatile anaestheticagents'
It is important for the anaesthetistto understandthe basicsabout the measurementprinciples
of the different gasesfor a better understandingof the monitor and to be able to possibly solve
a problem in the caseof technicalfailure, or to be ableto distinguishbetweenpatient failure
and technicalproblems.
Two gassamplinesystems
We distinguish nvo different ways to measurethe gasin the bröathing system.
At first, there is the mainstream BN monitor, which measuresthe gas directly in the breathing
system(fig. 1). A special measurementcha:nberis placedbetween the breathing system and
the tracheal tube, directly in path of the patients respiration gases.lnfra-red light shines
through the window of the cuvetteon one side of the adaptor and the sensorrecievesthe light
on the opposite side. BecauseCOz gas absorbsinfra-red light, the amount of infra-red light
which is detectedby the photo sensoris a measurefor the percentageCOz in the gas in the
measurins chamber.
BreathingSystem
Window
Scnsol
Fig. 1
Mainstream ffiared analYzer
An electrical cable connectsthe measuringchamberwith the monitor.
Thesemainstreammonitors have advantagesand disadvantages.Thesemonitors have a fast
response-time,
becausethereis no delay time.
The advantaeesare:
l. No gasis removed from the breathingsystem,so it is not necessaryto increasethe fresh
gas flow to compensatefor the removed gas.
Water and secretionsare seldom a problem with this analyser.
A standardgas is not requiredfor calibration.
The disadvantagesare:
1. The analysiscuvette must be placed near the patient. The sensorwill add weight and may
causetraction on the trachealtube.
2 . Becauseof the measuring cuvette,the breathing systemwill increasedead space.
J.
Leaks, disconnection and circuit obstructionscan occur.
4 . The sensormay becomedislodged from the cuvette. When partically dislodged theoÄ COz
reading may be incorrect although the wave form appearsnormal.
5 . The sensoris sensitive to damagee.g. when falling on the floor. Newer units are more
resistantto mechanical trauma.
6. The measuringchambersmust be cleanedand desinfectedbetweentwo patients.There is
danger for cross contaminationbetweenpatients.
A secondmethod to samplethe gas from the patient, we call side stream measurement(fig2).
In a side streammonitor the sensoris located in the monitor itself @) and a pump aspirates
ffi
Fig.
Sidesteam measurementprinciple
.2
gas from the sampling side (B) through a sampling tubing (C). Keeping the sampling tube as
short a possible will decreasethe delay time and result in more accuratewave forms of the
capnogram.
To avoid contamination of the monitor by water, manufacfurershave constructedwater traps
which must be emptied periodically. Other manufacturersuse nafion tubing which allows
water to diffuse through the wall of the sampling tubing.
The accuracy of these side streammonitors, decreaseswith increasingrespiratory rate e.g. in
small companion animals. Most side streamcapnographsare accurateuntil respiratory rates of
40 breathsper minute. Above 40 breathsper minute there is a slight decreasein end-tidal
accuracyand in accuracy of the wave form of the capnogrnm.Other factors that may affect
accuracyare the sampling flow rate and the imer diameter of the sampling tube. On some
capnographsthe flow rate can be varied. The flow rate should be proportional to the size of
eachpatient. It is advisable to conduct the sampleflow back into circle systemto save
anaestheticgas and to avoid contaminationof the operationroom.
In veterinary anaestheticpractice the side streamgas monitor is more popular comparedto the
mainstreamgasmonitor.
The advantagesof the side stream gas motitor are:
l. sampling from patientswho arenot intubatedis relativeryeasv.
2. Calibrationwith an accuratecalibrationgasis easily.
3. The patient interfaceis lightweight and inexpensive.
4. Thesedevicescan be usedwhen the monitor must be remotefrom the patient(e.g.,during
M.R.I.).
3
are:
Thedisadvantages
toUittgsamplesystemcanoccure.Secrationsor watercancause
th.
*th
T-r"blr*r
sothat waterentersthe
obstructionof the tubing-.Somewatertrapsmay be saturated
sYstem'
measurement
canoccur'
2. Leaksin thesamplingtubingor obstructionby kinking
systemor rreturnedto the
scanvenging
3. The gasesaspiraäamustbe eitherroutedto the
breathingsYstem.
4. SomedelaYtime is inevitable'
TechnoloKv
lnfra-redlight absorption
principleandwasdevelopedby
Theprincipl. of irrä-d üght absorptionis anold measuring
in a gasmixture'At thattime it was
Luft (19a3)in Germanyto ireasureittt CO, percentage
insidesubmarines'
importantio know the COzpercentage
havetwo or moredissimilaratomsin
Infra-redanalyzersur" bar"ä on the lact that gasesthat
havespecifi"Td Tuqueabsorption
themoleculelike coz, NzOandthehalogeniedagents,
is proportionalto the
.p""Ou of infra-redtiffrt. Sincethe amountof light absorbed
by comparing
of the absorbingmolecules,thecäcentrationcanbe determined
concentration
andOzdo
with that of a known stanäard.Thenonpolarmoleculesof nitrogen
the absorbance
usingthis technology'
not absorbinfra-redlight andcannotbe measured
llltttor
'C-i!
I
firrers
i
I
r n r r s hsto u ' c e
I
ilheel
äl-a:-ciopper
i
l ! l
f , e f e r e n cCe h e m b ! r
t!l
tit
lf at c I
tia
i
>[lccltonics
Phstoscnsot
Fig. 3
Sidestreamoptical infrared analyzet
of IR light is generatedby an IR light
Figure 3 shows a side streamI.R. analyser.A beam
This chopper wheel has holes
sourceand conductedthough a spinning weel: the chopper'
fn" gasto be measuredis pumped
with filters specially selecte-dfor ihe go;* to be measur.a'
chamber.The selectively filtered and
continously through a sample chamber:the measuring
and also through a referencechamberwith
pulsed light is passedthrough the samplechamber
focusedon an IR light detector: the photo
no absorptioncharacteristic-s.The IR tigttt i, then
gas is proportional to the partial pressures
sensor.The amount of tigtt absorbedu! tne sample
light Lvels on.tht photosensorproduce changesin
The
of the gasesto U. *"*,räd.
"h*g'irrg
amplifier processesthe signalto a
the electricalcurrentthat runs through it.ln etectric
perfect caPnogram.
Mono chromatic side streamIR analyzersuse one wavelength to measurepotent inhalational
agentsand are unable to distinguish betweenagents.When such an analyzeris used,the
anaesthetistmust select which agent is to be monitored. Polychromatic IR analyzersuse
multiple wavelengthsto both identify and quantify the various agents.This eliminates the
need for the user to select the agentto be monitored.
Most side stream analyzershave fixed sampling rates (usually 150 mVmin.). The measuring
cell is calibratedto zero, usually with room air and to a standardlevel using a calibration gas
mixture delivered by a small pressurizedcilinder. Some old types side stream capnographsare
sensitive for interfearing of N2O gas. Thesemonitors (e.g. Gould, Godart) have a knob ('Ttr2O
comp") which has to be usedduring anaesthesiawith Oz and NzO. The COz measurementat
that momentis compensatedfor NzO interfearing.
C h o D Dl rl hr e eI
SampC
l eh a m b e r
IR
Source
P o wre
Sutply
lR Iight
filter- 0etector
Airway
Fig.4
Mainsüeam infrared analyzer,cross-sectionalview
Figure 4 shows the measuringprinciple of the mainstream CO2 measurement.As was showed
before, the patient respiratory gas streampassesthrough a chamber (cuvette) with two
windows, usually made from sapphirewhich is transparantto infra-red light. The cuvette is
placed betweenthe breathing systemand the patient. The sensor,which housesboth the light
source and detector, fits over the cuvette. To prevent condensationof water, the sensoris
heatedslightly above body temperature.IR light shinesthrough the window on one side of the
adapterand the sensorreceivesthe light on the opposite side. After passingthrough the
sample chamberthe light goesthrough three ports in a rotating wheel, which contains (a) a
sealedcell with a known high CO2concentration,(b) a chambervented to the sensor's
internal atmosphere,and (c) a sealedcell containing only nitrogen. The radiaton then passes
through a filter that screensthe light to the correct wavelength to isolate COz information
from interfering gasesand onto a photo detector.The signal is amplified and sent to display
module.
Photoacousticspectroscopy
Photoacousticspectroscopieis basedon the fact that absorptionof IR light by molecules
causesthem to expandand therebyincreasesthe pressureof the gas.If the light is deliveredin
pulses,the pressureincreasewill be intermittent.If the frequencyof pulsationis in the audible
5
range,the changesin pressurewill createan acousticsignalthat can be detectedby a
microphone.A photoacousticgasanalyzeris shown in fig. 5.
tlcrcphoac
r.ä'hIt t
PrtlGlt
oü
blct
Fig.5
uEp-loo.
Rofcrcacc
():5rgca
Rafctcace
Gü
Irlct
Photoacousticffiared analyzer
The gas sampleis drawn into the merlsurementchamberthrough a flow regulator. This makes
the sample flbw rate independentof changesin the patient's airway pressure.Light from an
infra-red sourceis aimed toward a window in the measurementchamber.Before the light
entersthe chamber,it passesthrough a spinning chopperwheel that causesit to pulsate.To
differentiate betweenthe three signalscausedby carbon dioxide (COz) nitrous oxide (NzO)
andanaestheticagents (A.A.), the chopperhas three concentricbandsof holes. This causes
the light to pulsateat three different frequencies.Each light beam then passesthrough an
optical filter that only allows light of a specific wavelength to passthrough. Thus the
frequenciesand wavelengths of the incident light are matchedto the infra-red spectraof the
three gasesto be measured.[n the measurementchambers,eachbeam excites one of the
gases,causing it to expand and contract at a frequencyequal to the pulsating frequencyof the
appropriateinfra-red beam. The periodic expansionand contraction of the gas sampleproduce
a fluctation of audible frequency that can be detectedby a microphone. The oxygen
concentrationin this monitor is estimatedaccordingto the paramagneticprinciple. This
principle will be explained later on. Becauseof the switched magnetic field, again a sound
wave is produced.The amplitude of this wave will be proportional to the concentrationof the
02 present.
The photoacousticprinciple was developpedby a Danish company Bruel and Kjaer, a
company which produced high quality professionalmicrophones.Later on Hewlett Packard
producedthis multigasmonitor in licence.This type of monitor usesa specialselectedinfrared band with for anaestheticagentconcentrationmeasurement.This is shown in fig. 6.
A bandwidth 10 - 13 pm (micrometer)wavelengthwas chosenwhile most other
commerciallyavailablemultigasmonitorsusea bandwidtharound3,3 pm. To usethe
bandwidthof 10 - 13 pm has specialadvantage.The problem is that herbivoreslike horses,
sheepand cows producemethane(CH4)in their intestinesand consequentlyin the expiration
gases.The uppercurve of fig. 6 showsthe absorbance
of methanein the infra-red spectrum.
wavelength
7
Capnomac
bandwith
Fig. 6
AGM1304
bandwith
Diagram representingabsorptionof methane(CHa) and halothane in the infrared spectrum. The
bandwidth used by two different anaestheticagentmouitors is indicated.
We see alarge absorptionpeak around 3,3 pm. The lower curve shows the halothane
absorption curve of the infta-red light. We seea small absorptionpeak at 3,3 pm and a large
absorptionpeak betwee4 10 - 13 pm for halothane.This results in interferenceof methanein
the halothanemeasurementfor all the multigas analyseswhich use 3,3 pm as a wavelength.
Thesemultigas monitors cannotbe used at horsesand herbivores,becausehalothane
measurementis incorrect. Methane is detectedby this gas analyzer as halothaneand added at
the normal halothaneconcentration.Examplesof this analysersare: Datex multicap, Datex
capnomac,Datex AS/3 old model, SiemensSC9000monitor and others. The influence of
niethanedwing isoflurane measurementin this type of monitors (3,3 pm) is not so dramatic
and is seventimes (7 x) lower comparedto halothanemeasurementin the samemonitor.
The sensitivity for methane of a multigas analysercan be easily tested.Make for this test a
gasmixture of L,Zo/o
natural gas (which consistsof 80% CFI4)and 98,8o/oair in an anaesthesia
the
sampletube
When
of the analyzeris connectedto the gasmixture,the multigas
balloon.
monitor with the 3,3 pm bandwidth will show a false "halothane" reading of > 10oÄ
'halothane". At the same time when
switched to "isoflurane" the reading will be 2%ofalse,
isoflurane switched to enflurane,desfluraneor sevoflurane,these false measurementsare
respectively2,5%o(Enfl.), 1,5%@esfl.) or 1,3Yo(Sevo).Remark that this test is donewith 1%
CII+ which equalsto 10.000ppm (partsper million).
The samemethanelesl with a 10 - 13 pm bandwidthmultigasmonitor will show not any
false reading for halothane,isoflurane, enflurane,desfluraneor sevoflurane.
Example,of non-methanesensitiveanalyzersare:Bruel and Kjaer type 1304multigas
analyzer,Hewlett Packard M1025 AnaestheticGas analyzerand others.
Summarizing the photoacousticspectroscopy,the next advantagescan be noticed:
Better long-term stability than traditional lnfrared insfruments
Accuracy is greater comparedto I.R. technology
Not sensivefor interfering gaseslike methaneor alcohol
Excellentzero stability
Short warmuptime (someminutes)
As a disadvantagecan be mentionedthat the pricesof this gas analyzersare higher compared
to I.R. analyzers.
+
Electrochemicalanalysis
The electrochemicalanalysisis one of the oldestmethodsto estimatethe Oz percentageof a
gasmixture. The 02 analyzerconsistsof a sensor,which is exposedto the gasbe sampled and
Fig. 7
Electochemical 02 analyzer
the analysorbox,which containsthe electric circuit, display and alarms.The sensor, frg. 7,
contains a cathodeand an anodesurroundedby electrolyte gel. The gel is held in place by a
membranethat is non-perrneableto ions, proteins or other such materials,yet permeably to
gasessuch as Oz. The membraneshould not be touchedbecausedirt and greasereduce its
usablearea.
Oz diffuses through the membraneand electrolye to the cathodewhere it is reduced, causing
a current to flow between the electrodes.The rate at which Oz entersthe cell and generates
current, is proportional to the partial pressureof 02 in the gas outside the membrane.This
current is amplified and the meter displays percentage02. These analyzersrespond slowly to
changesin Oz pressureso that they cannot distinguish betweenin- and expiration percentage.
The measuringresult will be an averagevalue betweenthesepercentages.
There are two basic fypes of sensors:galvanic cell andpolargraphic electrode.
Galvaniccell
A galvaniccell (or fuel cell) sensoris shownin fig. 7. It consistsof a lead anodeand a gold
cathodesurroundedby potasium hydroxide electrolyte.The cathodeacts as the sensing
electrodeand is not consumed.The hydroxyl ions (OH-) formed there react with the lead
anode,forming lead oxide. The lead anodeis gradually consumed(worn out).
Cathode:
Oz+ ZHzO+ 4e' +
Anode:
4OH + 2pb ->
4OH2pbo + ZHtO+ 4e-
The galvanic sonsorcomes packagedin a scaledcontainer from which Oz has been removed.
Its lifespanbeginswhen the packageis opened.Its useful life is cited in pecenthours,which
is the product of hours of exposwe and 02 percentage.Sensorlife can be prolonged by sealing
when not in use or preserving in a low oxygen environment. Thesesensorsrequire no
membraneor electrolytereplacement.The entiresensormust be replacedwhen it becomes
exhausted.Thesesensorsarerelatively expensive(t 200 Euro).
P o ü! l
Sourcc
Ilectrolttc
E l a s sI n s t l l a l o r
Fig. 8
Polarographic 02 sensof
P c r m c rlac!
!mbranr
Polarographic Electrode
Another method to estimate 02 percentageis possible by using the polarographic sensor
(Clarkelectrode)fig. 8. It consistsof a silver anode,a gold or platinum cathode,electrolyte
and a gas-permeablemembrane.Oz diffuses through the membraneand electrolyte to the
cathode.When a potential difference is induced by a battery betweenthe anodeand the
cathodethe oxygen molecules are reducedto hydroxide ions. The current betweencathode
and anodewill be proportional to the partial pressureof Oz in the anaestheticmixture.
Cathode:
Oz+ 2HzO+ 4e' -+
Anode:
4Ag + 4Cl- --+ 4AgCl + 4e-
4OH-
polarographic sensorsare units that can be disassembledand reusedby changingthe
membraneor electrolyte. The sensorremains unconsumedwhen not turned on, so the
analyzer should be kept on standbywhen not in use.
ln somemonitors the polarographicprinciple for Oz measurementis combined with an I.R.
COz measurementlike the Datex nofinocap, which is used in many veterinary practices.
Summarizing the electrochemical analysisforOz measruement,the next advantagescan be
concluded:
l. These instruments are relatively simple and not so costly to purchase
2. Comparedwith other technologiesfor measuring02, the electrochemicalanalyzeris
compact and takes up little space
3. Warmup time is short.
The disadvantiges are:
1. These instrumentsrequire regular maintenancee.g. membraneand electrolyte changesor
galvanic cell replacement.Theseall dependingof usersintensity
2. Calibration is required before use, eachday in ay (21% Oz) md 100% Oz
3. A study found that electrochemical malyzers had a high percentageof errors,most
commonly causedby humiditY
4. The analyzershave a slow responsetime (some seconds)and cannot be usedto measure
end-tidalOz.
1
ParamaexeticAnalysis
A different method to measure02 concentrationsis based onthe paramagnetic analysis.
When induced into a magnetic field, some substanceslocate themselvesin the sfongest
portion of the field. These substances
are termedparamagnetic.Of thegasesof interestin
anasthesia,
only 02 is paramagnetic.The Oz moleculecan be seenas a moleculewith
magneticproperties(comparablelike iron molecules).
When a gas containing 02 is passedthrough a switched magnetic field, the gas will expand
and confract, causing a pressurewave proportional to the partial pressureof 02 present.To
obtain a high degreeof accuracyit is necessaryto comparethe pressurein the gas sample to a
referencesignal obtained using air.
U!rtron.gnrt
llrrtürr (}ut
*"n"''
)
''''o
0 i l fr r ! n t i a l I r r n t d u c c t
R r l r r ! n c ! G e sl r
Fig. 9
Paramagnetic 02 analyzer
A paramagnetrc Oz analyser is shown in fig. 9. Reference(air) and sample gasesare pumped
through the analyzer.The two gaspaths arejoined by a differential pressureor flow sensor.
The magnet is switched on and off rapidly. If the streamsof sampleand referencegas have
different 02 partial pressures,the magnet will causetheir pressuresto differ. This difference is
detectedby the transducer and convertedinto an electrical signal that is displayed as 02
partial pressure(or convertedto volumespercent).The short rise time (100-200m. sec)of this
techniqueallows measurementof inspired and end-tidal Oz levels at high respiratory rates.
The paramagneticanalyzer is strongly temperaturedependent;therefore accuratetemperature
compensationis needed.Somemonitors (e.g.Bruel and Kjaer, Hewlett PackardMl025)
combine photoacousticinfrared analysisof COz,NOz and anaestheticagentswith
paramagnetic Oz analysis. Switching the magneton and off at a certain frequency generatesa
pressurewave that can be detectedin the acousticspectrum.This is known as
One problemwith theseinstrumentsis that if the gas from the analyzeris
magnetoacoustics.
retumedto the breathingsystem,or to the low flow or closedcircle system,the air that is used
as a referencegaswill dilute the other gasesand causean increasein nitrogen.
Piezo electricAnalysis
The piezo electric method is usedto measurethe concentrationof the anaestheticagents.This
method usesvibrating crystalscoatedwith a layer of lipid or thin silicon rubber,seefig. 10.
One crystal is coatedand one crystal is uncoated.When exposedto a volatile anaesthetic
agent, the vapor is adsorbedinto the lipid- or silicon layer. The resulting changein the mass
of the lipid- or silicon layer, alters the vibrating frequency of the coatedcrystal. By use of an
electronic systemconsisting of two oscillating circuits, one of which has the uncoated
(reference)crystal and the other a coated (detector) crystal, an electric signal which is
proportional to the vapor concentrationis generated.By comparing the vibration frequencies
of the cristals, the levels of anaestheticagent in the gas being analyzedcan be measured.
6rs Ilcr
Unsosltd
Crystrl
il!ctt0nics
0 i s p l lt
Cort!d
Srtst.l
A
Fig. 10 Piezoelectric anralyzerfor anaestheticagents
Advantages
1. Investigationsshow an accuracyof better than0,l%o
2. Fast responsetime - newer models can measureinspired and expired levels of agents
3. Short warm up time
4. Compact - the units are smallDisadvantages
1. Only suitablefor the anaestheticagents
2. No automaticagent identification
3. Water will causeeffors with the piezoelectricmonitor. In the sampling tube, water
separatorsor nafion tubing must be used.
Mass spectromebry
The massspectrometer canbe usedto measureinspired and end tidal concentrationsof Oz,
Nz, COz, N2O, argon, helium methaneand the anaestheticagents.The mass spechometer
differs from most other measuringdevicesin that it measuresconcentrationsin volumes
percent,not partial pressure.Fig. 11 shows a block diagram of the mass spectrometer.In this
apparatus,gas sample from thelatient is exposedto a vacuum of approximately 10-6mm Hg
0 CA m t l i l i e t
Analtler
to
tttta
t.rt,
l o n i r a t i o nC h a r n b e t
PünP
Cathodr
Inlrl
Irhaust
S a m pP
l rr m P
Fig. 11 Magnetic sectormassspectrometer
after passingthrough a valve to an analyzing charnber.At that hard vacuum, the gas
molecules in the ionization charnberare bombardedwith a high energy electron beam,
resulting in the gasmolecule's being ionized or charged.The ionized gas is then accelerated
by a high voltage eleltrostatic field and allowed to passthrough a very strong magnetic field.
When a chargedparticle passesthrough a magnetic field, the path of the particle is bent. The
path of particles with high chargeto massratio, are bent more than the path of particles with
low chargeto massratio. If the electronbeam is tuned correct, almost all the ions will have
the samechargeof -1. Thus, the degreeto which a particle'spath is bent as it passesthrough
the magnetic field is a function of the massof the particle. Light particles (moleculeswith a
light mass) curve sharply, whereasheavy particles (moleculeswith healy mass)curve less
sharply. If collector plates are placed strategicallyalong the possiblepathways that charged
molecules can take, the mass spectrometerneedsonly to count the number of particles hitting
eachcollectingplate, add them together,and devideeachplate's countby the sum of all the
collectingplates' counts.The result is the relativeconcentrationof eachtype of moleculein
the patients respiratory gas. Despite the seemingcomplexity of the description,mass
spectrometergenerallyworks quite well.
B
Becausethe typical mass spectrometeris quite large and expensive,they are usually timesharedamong multiple anaesthetizinglocations (see fig. 12) by rurming long sample lines
from the operating room site to a central location where the mass spectrometerresides.This
shared massspectrometeris located centrally. Long sampletubings passfrom each sampling
location (the operating theatre)through specially installed ductwork to the multiplexer, which
sequentially directs sample flows to the massspectrometer.Information derived centrally is
relayed to the individual stationsand displayed.A typical monitoring duration on any given
patient is usually 15 to 20 secondsbeforethe systemswitchesto monitor anotherpatient.
This sharing, or multiplexing, of the mass spectrometerresults in significant cost savings
comparedwith having a mass spectrometerdedicatedto each anaesthetizinglocation, but such
a system does not provide continousmonitoring for eachpatient. Generally the high cost of
mass spectrometersystemsand their inabilify to continuously monitor every patient on the
systemhas resultedin a decreasein their popularity.
PalientDisplays
MassSpestmneter
Fig. 12 Sharedmass spectrometer
Advantages
Nearly every gas of importance to anaesthesiacan be measured
The responsetime is fast enoughto allow end tidal measurementse.g. a stand-alonemass
spectrometercan accuratelymeasureexpired gasconcentrationsin subjectsrequiring tidal
volumes as low as 3-4 ml and at respiratoryrates up to 80 breaths/min
Reliable functioning for long periods
Since the massspectrometercan measurenitrogen, it can detect leaks in the aspiration
mechanismand increasesin nitrogen in the breathing systemwhich could result from an
air embolus.
I
I
t3
Disadvantages
With a mass spectrometer,the reliability of the readingspresupposesthat no gas other
than those for which it is programmedare presentin the gas sample. When an unmeasured
(not programmed) gas is introduced (e.g. methaneproduced by herbivores) into a m:Ns
spectrometer,the concentrationof the measuredgaseswill be erroneouslyhigh and gases
not presentmay be reported. Carbon monoxidecannot be measureddirectly by the mass
spectrometer.This gas can be generatedin a dry COzabsorbentwhich reactswith
isoflurane or desflurane.This dangerousgasresults in a small increasein nitrogen and
COz readingsand the massspectrometermay incorrectly indicate enflurane.
The gas aspiratedmust be scavenged.It cannot be reftrmed to the breathing system. The
fresh gas flow may need to be increasedto compensatefor the gas removed.
The mass spectrometerrequiresa fairly long warm-uptime.
Raman Spectrometry
In Raman spectrometry (light scatteringgas analysis)a laser emits monochromic light. When
the light interactswith a gasmolecule that has interatomic molecular bonds, some of its
energy is converted into vibrational and rotational modeswithin the molecule. A fraction of
the energy absorbedis reemitted at different wave lengthsin a phenomenoncalled Raman
scattering.The magnitude of this shift is characteristicfor particular molecules, enabling their
identification. This effect is known as Ramanscattering after C.V. Raman who predicted it on
theoretical grounds in 1923 and demonstratedn 1928in the leadingjournal "Nature " by the
article "A new type of secondaryradiation".fNature 1928,l2I:105).
This Raman scattering was commercializedin the last decenniumin the "Rascal 1" monitor
sold by Ohmeda.This technology can be applied to all gaseslikely to be presentin the
respiratory gas mixture, including CO1 Oz,N2, N2O and the anaestheticagents.Fig. 13 shows
the block diagrarn.
Sample cell
Ai'
Dam Sample
Sarnple
Iu
Out
In
Sample
Out
Air
Dam
In
Window
ttirror
oo
oo
Window
Photon
Counting
Circuits
Fig. 13 Raman light scatteri:rggas analyzer
oo^öo
o o-
oo
,l
The gas mixture to be analysedis drawn continuously through a water separatorinto the
instrument. The measwing cell is a cylinder with a window at each end. The light is generated
by a helium-neon laser. Two mirors increaselight intensity within the cell. The illumination
is so powerful that it could combust the anaestheticagents.To prevent this, room air is drawn
into the cell close to the windows, creating an air dam acrossthe windows.
There are port holes on the side of the sample cell. Each has a frlter of narrow optical
bandwidth, tuned to a specific Raman scatter frequency.Transmitted light is detectedby
photo diodes.The number of photons at eachwavelength is directly proportional to the
concentrationof the particular gas present.
Advantages
This technology can identiff and measureinspired end expired partial pressuresfor most
gasesof interest in anaesthesia.
Fastresponsetime.
Fast start up time.
High degreeof accuracy.
Unknown or unusual gasessuch as methaneor alcohol do not interfere and don't affect
the accuracy.
Disadvantages
The analyzeris fairly large and heavy compairedto LR. monitors.
Air will be added in the returnedbreathing gas. In low flow or closed system anaesthesia
the sampleout gas cannot be returned.
This technology is relatively new in commercially available instruments(+ 10 year); the
initial co3t of the monitor is somewhathigher than with other technologies.Also technical
problems with the laser were reported.
ChemicalCarbonDioxide Detection
ihemical (colorimetric) indicator devices consistsof a pH sensitivechemical indicator whose
pH is just abovethe level wherethe dye chosenis expectedto changeits colors enclosedin a
disposablehousing.When the detectoris exposedto CO2,it becomesmore acidic and
changescolor from pink (low COz) to yellow (high CO2).
The inlet and outlet parts are 15 mm, so the device can fit betweenpatient and the breathing
system.The chemical COz detectoris used primarily for confirming successfultracheal
intubation:
A minimum of six breaths should be performed before a determination is made.
This devicecan function durine 10-24hours.
Advantages
The deviceis easyto use.
The deviceis very cheap.
Requiresno power source.
Very accuratein diagnosingesophagealintubation.
Device can indicateeffectivenessof resuscitation.A negativetestresult may indicatepoor
or absentpulmonaryblood flow.
Disadvantages
The deviceis not suitablefor continuousmonitoring.There is no wave form or alarm.
Not suitablefor very low tidal volumes.
t5
IJV lieht analvzer
Ultra Violet Light is absorbedby halothane.Comparableto the side stream optical infrared
analyser,one of the first halothaneconcentrationmeasuringdeviceswas basedon the U.V.
absorptionprinciple. It was the "Hook and Tucker" halothaneconcentrationmonitor which
was well known in the sixties and seventies.
U.V. light is absorbedby many gaseswhich are usedin the anaesthetic
practice.So it is
important to choosea wave length of the U.V. spectrumwhere other gasesdo not affect the
halothanemeasurement.This early halothanemeasurementswere done at 2500 A
(1 Angström: l0-10meter) andnät affectedby Oz,NzOor COz.
'li:1
.{.
\:'I ,/
t{-\.
Y-j
+,
)
But he is getting3xMAC.......
Someproblemswerereported,causedby methane,when3,3 pm I.R. analysersareusedin
herbivores,
-Infrared analyzer
-Photoacousticinfrared analyzer
-Mass spectrometer
-Raman light scatteing analyzer
-Chemical/hygroscopic
NzO
-lnfrared analyzer
-Photoacoustiqinfr ared analyzer
-Mass spectrometer
-Raman light scatteing analyzer
Oz
-ParamagneticOz analyzer
-Mass spectrometer
-Elecko chemical 02 analyzer
-PolarographicOz sensor
-Mass spectrometer
-Raman light scatteing analyzer
Nz
-Mass spectrometer
-Raman light scattering
AnaestheticAgents -Infraredanalyzer
(Hal,Iso,Des,Sevo)-Photoacoustic
infraredanalyzer
-Massspectrometer
-Raman light scatteringanalyzer
-Piezo electric alrralyzer
-W light analyzer
CO
-Indirectly with mass spectrometer
Methane
-Indirectly with short wavelength(3.3 pm) infrared
analyzer
-Mass spectrometer
Acknowledgements
The author thanks miss B. Rietbergenfor editing the text.
References
J.A' Dorsch,M.D. , S.E.Dorsch,M.D. UnderstandingAnaesthesiaequipmentEd. 4lggg
Williams and Wilkins
L.J. saidman,M.D., N.Ty.smith, M.D. Monitoringin Anasthesia.
Ed. 3 rgg3
Butterworth-Heinemann
Y. Moens, W. Verstraeten.Capnographicmonitoring in Small Animal Anaesthesia.J. of
Am. Anim. Hosp. Assoc.(1982) 18, 659-67g
Y' Moens, A. de Moor. Use of infrared carbondioxide analysisduring generalanaesthesia
in the horse.EquineVet. J. ( I 981) 13, 229-234
Y. Moens, P. Goodes,E. Lagerwerj.The influenceof methaneon the infrared
measrrementof halothanein the horse.J. vet. Anaesth.(1991)l9,4-7
P' Gootjes,Y. Moens' A simple methodto correctinfraredmeasurement
of anaesthetic
vapour concentrationin the presenceof methane.J. Vet. Anaesth.(lgg7)
24.24-25
Principles of PressureMeasurement
PressureScalesand units
Thereare three pressurescales:
1. Absolutepressure
2. Gaugepressure
3 Vacuum
Absolutepfessureis measuredrelativelo no pressureat all (a perfectvacuum),andhenceis alwayspositive
Gauge pressureis measuredrelative to atrnosphericpressure,but is generallyonly used for pressuresabove
atmospheric,
so it's alsopositive.
pressure,
Vacuumis usedfor pressures
belowaünospheric
downto no pressureat all (a "perfect"vacuum).
AT ltos P6ۧlc
?ltt55ut8
fgfAL
vACUot{
po3tTlVE
Pß133 UET
AESOLUTI, Pßt65UEE
, v A C UU n Units of pressure:
PositivePressure.
The SI unit of pressureis the Pascal,which is definedas the pressureexertedby a force of lN over an areaof I
squaremetre.This is a very small pressureso the multiple, kiloPascal,(kPa) is commonlyused.For a standing
human,meanbloodpressurewould be about7 kPaat his headto 27 kPaat his feet.
The imperialunit of pressureis the pgi or poundforceper squareinch (lbf in-21.I psi = 6895Pa. The suffrxg is
pressure
used,specifyinga gaugepressure.
sometimes
is about14.7psi,or about101300Pascals.
Atrnospheric
Thembaris anothercommonunit of pressure.
Standardarnosphericpressureis 1024mbar.
Smallpressures
arealsomeasuredin termsof the equivalentverticalheightof a liquid: The pres$ueat the baseof a
columnof liquid is givenby pgh,wherep is the densityof the liquid, g is the acceleration
dueto gravity,andh is the
verticalheight.(Notethattle pressureis independent
of the diameterof the columnof liquid).
Atmosphericpressureis supportedby about 10.3metresof water, or, more conveniently,by about 760 mm Hg
(because
thedensityof mercuryis 13.55timesthatof water.)
Measurements
madein this way areoftenreferredto as"pressurehead"or just "head"of a particularliquid, usually
water or mercury.Note that a manometerfilled with the fluid whosepressureis to be measuredwill give a head
readingin termsof thatfluid, so if measurements
arerequiredin termsof cmH20,for instance,thena cosectionrnust
be madefor the relativedensityof the fluid. Rememberalso that if the manometeris at a different height to the
site,thenthe connectingü.rbewill alsohavea pressure
measurement
headassociated
with it.
CmHzOis a commonunit in anaesthesia.
l0cmH20= 1 kPa"= 7 5 mmHg.
I mbar= 0 75 mmHg= 0.4 inchesH20
lmmHe= 133.3Pa
Vacuum.
pressureto zero pressure.It is generallyexpressedas a negativeheadof a
The vacuumscaleis from atrnospheric
particularliquid, or in Torr.
I Ton = I mm Hg, andafnosphericpressure= 760Ton
Sothe smallertheTorr...the greaterthevacuum.
Methodsof Measuring Pressure
There are four piecesof equipment used in anaesthesia:
I
The U tube manometer has equal heights of a liquid in each arm. When a pressure(positive or negative with
respect to atrnospheric) is apptied to one arm, then the difference between the heights in the two arms is the
pressure (or vacuum) head in terms of the liquid in the manometer. The manometer therefore measuresgauge
pressure,but if one nrbe end is sealed with a perfect vacuum (a Tonicelli vacuum), then the device measures
absolute pressure,and is called a mercury barometer.
P
1
ußElPßrss
r{sAD l_
The mercury column (sphygmomanometer)
is a mercurymanometerbut wittr only onecolumn.Theotherside
is a reservoirof largediametersuchthat the appliedpressuredoesnot changethe level in it significantly.It will
only measurepositivepressures.
PRTSSUßE
HIAD
The.pressuregaugecontainseithera diaphragrn,for low pressures,
or a curvedandflattenedtube,(a Bourdon
tube). Increasingpressureextendsthe diaphragmor straightens
out
-absolute. the tube. This movementis linked to a
pointerwith a scale.It measures
gaugepressureratherthan
(The aneroidbarometerworkson t1,esame
principle,but with a sealeddiaphragm...and
doesmeasureabsolutepressure.)Its sister,the vacuumgauge,has
the sameoperatingprincipleexceptthatvacuumtendsto straightenthetubeout.
P
..--->
The pressuretransducer consistsof a thin diaphragmwhich deflectselasticallywhenpressureis applied
to it.
This deflectionis detectedby straingaugesmountedon the surfaceof the diap-hragrn
äa tn" outputamplified
electronically.Another class of deviceshave a diaphragmmade from a semiconductor
whoseresistanceor
chargepropertieschangewith strain.
Pt
sTßDlF,
G A oc 8 3
Pressuretransducerc
What is a strain gauge?
. . . .. ..4 straingaugeis a grid of thin wire, laid up and down on an insulatingbackingandgluedto the surfacewhose
strain is to be measured.The surfacestrainis thereforereproducedin the wire, with two effectson it; firstly the
go€sup becausethe total lengthof the wire hasincreased,
resistance
andits diameterhasdecreased,
andsecondlythe
propertyof
resistivityof the wire increases,againincreasingthe resistance.
@esistivityis the fundamentalresistance
thewire....it'sdifferentfor eachmaterial).
So you just measure the change in resistanceof the gauge?
... .. ..Not quite: the changein resistanceis very small and is hard to measurereliably. A circuit called a Wheatstone
bridge is used. This consists offour equal resistors (or in our case, strain gauges)ananged in a square:
OOTPVT
. . . . . .A constantvoltageis appliedacrossonediagonalof the bridge.If the four resistorsareidentical,therewill then
resultsin a voltageon this
be zerovoltageacrossthe otherdiagonal,but any slight variationin one ofthe resistances
that a straingaugegives,the outputis only a few millivolts, but its mucheasier
output.For the changesin resistance
to amplifo andthenmeasurea smallvoltagethanit is a smallchangein resistance.
Where are the otherthree resistors?
... ...In fact all four resistorsare straingauges,andthey all contributeto the measurement.
The oppositestraingauge
to the one aboveis also mountedon the diaphragm,therebydoublingthe outputfrom the device.The other two
strain gaugesare either mounted somewhereon the diaphragmwhere they measurecompression,and so.also
contributeto the output,or they aremountedon an unstrainedpartof the assembly.
They are still importantbecausethe deviceis sensitiveto thermalstrain,andif the temperatureof only one arm of
eventhoughthe pressurehasnot changed.
the bridgechangesthenan outputwill be generated,
Sothe wire comingfrom the trensduccronly hasa very small voltageon it?
. . . .. .YES, so its worth thinking aboutwhereyou aregoing to put it: If the wire is longerthan you need,coiling the
excessup andhangingit on a convenientlight switchis not a brilliant idea(don't laugh,it hasbeendone).
Try to arrangeleadssothat they don't run alongsidemainscables,or anythingcarryinga high voltageor current,as
any cable acts as an aerial, and the noisepicked up can be significantcomparedto the small signal from your
transducer.
Is this what is meantby signal to noiseratio?
... ...Yes. The cablefrom the transduceris shielded,meaningthat thereis an outerbraidedconductivelayer around
the wires carryingthe sigrral.This outerlayer is connectedto earth(at one end only) and it protectsthe wires from
it isn't perfect.Thelargerthediameterof thecable,thebetterthe shielding.
electricalnoise....but
the signalfrom themis small,so the cablehasto screenit from
......This principleappliesto a lot of transducers:
havea smallamplifierbuilt into them,so tlat the sigrraltravellingbackup the wire
noise.Somemodemtransducers
is still the same,the sigrralto noiseratio is improved.
is larger.As the interference
Instrumentation
What happensto the signalthen?
(a few
it from a millivolt signalto somethingmoreeasilymeasured
.......I1goesthroughan amplifierto increase
volts). Schematically,
an amplifierlookslike this:
.,...Gain is definedas the ratio of the outputto the input. Gain controlsmay be discrete(selectionof a particular
range)or continuous,via a knob.Gainis thegradientof thegraphbelow:
, ilcßEAslN G
6Ain
OVTPVT
INPOT
A continuous gain control is normally used in conjunction with a CAL button on the amplifier box. Pressing this
button unbalancesthe Wheatstonebridge on the transducerby changing the resistanceof one arm with an additional
resistance.This resistanceis known and stablewith time. The calibration knob is then adjusted to achieve the correct
output for this artificial input. The CAL button therefore calibrates the instrumentation and will detect most of the
failure modes of tle transducer.
. .. . . .fuld offset (or balance,or zero,or null) is wherethe graphcrossesthe Y axis. An offsetcontrolallowsyou to
setzerooutputfor zeroinput. For a straingaugetransducer,
manufaauringtolerancesandthermaleffectsmeanthat
tlre four straingaugesmakingup the bridgewill not canceleachotherout perfectlyatzeropressure.Also on the gain
graph above,the lines for different gainsdo not crossat zerooutput(generallybecauseof internaloffsetsin the
stagesof the amplifier).The resultis that if the gain is adjustedafter settingthe zero.. . .thezerowill often requirere.
thegaina little bit more.Theadjustments
adjustnent....and
to eachcontrolshouldbecomesmallereachtime round.
An offset canalsobe usedto null out a meanlevel of pressurefor measurement
purposes(althoughthe rangeof the
balancecontrolin an amplifieris usuallysmall comparedto the full scaleoutput).Largeroffsetsmay be rernovedby
(seebelow).
AC couplinginto an oscilloscope
Steticand dynamicsignals,bandwidth.
Pressuresignals(andthe signalsfrom manyothertransducers)
havetwo components,
staticanddynamic.
The staticrcmponentis the steadystatelevel of the signal,sometimesreferredto asthe DC (from the Direa Current
electricalsignal).
The dynamiccomponentis the partthat changesin time, sometimesrefenedto asthe AC (AltematingCurrent).The
alternatingcurrentin the mainssupplyto your housein a sinewaveat 50 or 60 Hz (dependingwhereyou live). Most
real AC signalsfrom a transducerare more complicatedthan a singlesinewave.Fourieranalysistells us that any
repetitiveAC signal,no matterwhat its shape,canbe represented
by a seriesof sinewaves,of differentfrequencies
andamplitudes.
A signalthatlookslike this in thetime domain:
I
AN?L'TUDE
I
('T>
Looks like this in the frequencydomain:
wss
-
2tT
FßEQueilct +
Similarly, the complex shape ot a blood pressure recording may be converted into a set of sinewaves. The
mathematical process tlat translates a signal from the time domain to the frequency domain is called the Fourier
Transform.
The relevanceof this is that, in orderto makean accuratemeasurement
of pressure(or anythingelse)we mustensure
that all partsof our measurement
systemarecapableof passingall the frequencies
ihat urein it e sourcesignal.This
is known as bandwidthIf any part of the systemtrasinJufficiät bandwidth
thenthe higherfrequencies
will be lost,
anda signalwhichshouldlook like this:
Will look like this.
This loss of bandwidthmay be electricalor mechanical:
Electricd Bandwidth
The instrumentation may contain filters to remove high frequency noise..The
frequency responsecurve of a lowpass
filter (meaning that it passeslow frequenciesand r"tnäues nigh onesyis
shown befow in the frequency domain;
OUTPUT
I lüP uT
svtoFF
FßtAueh/ey
The more sophisticatedLhe {ilter, tle steeper the response line above
the cutoff frequeacy, and hence the more
complete the removal of higher frequenciei. other filfering strategies
are highpass -i o-äp"rr. Bandpassmeans
that it passesa particular band of frequencies and removei all ot-hers(ike
the gaphic equaliser controls on your
stereo).
L
Unintentional Filters
The simplest filter network is a capacitor and a resistor:
Low
r{
rrä 9AsS
röJ>
ä | GB
?h35
The filters in your equipmentwill be more sophisticated
than this, but bewareof introducingstray capacitanceor
into a circuitwhenmodifoingleadsetc...asyou maymakea filterl
resistance
coupling
Oscilloscope
An oscilloscopehastwo inputsDC andAC coupled:the DC input transmitseverything,whereasthe AC input is via
a seriescapacitorin the instrument.This capacitorpassesAC signals(abovetypically 2-5 Hz) but not DC ones.The
AC input thereforefilters out the DC level and allowsthe AC signalto be viewedat a largermagrificationon the
screen.
Mechanicalbandwidth
One of the basic elementsof vibrationtheory is the seriesmasVspringsystem.The frequencyresponseof sucha
svstemis shownbelow:
OUfPVT
ßE5oNtrl.rcE
FßeauE
At frequencieswell below resonance,
the input stimulusis transmittedfaithfully to the output. At the resonant
frequency,the outputis much grcaterthan the input and at frequenciesabovethe resonantfrequencythe outputis
muchlessthanthe input.The heightandwidth of theresonantpeakaredeterminedby the dampingin the system.
lncreasingthe stiffnessofthe spring,or decreasing
themass,raisesthe resonantfrequency.
Bandwidth of pressure measurement devices
The manometer, mercury column and pressuregauge all have a low bandwidth:
The manometer has a large mass (the fluid in the tubes) connect€dto a soft spring (the restoring force is gravity) and
hence a low resonantfrequency. This can be seen by applying a pressureand releasing it suddenly: watch the fluid
column seesawback to zero.
The diaphragm in a pressure gauge is a soft spring. The Bourdon tube of high pressuredevices is stiffer but the
bandwidth is limited by the linkage to the needle.
The pressure transducerhas a much higher bandwidth but mechanical filtering may occur in the catheter or in the
(manometer) tube to the transduceri
. ..The diaphragm of the transducer deflects elastically when a pressure is applied to it. It is, therefore, a spring,
although a stiff one. Connected to this spring is a column of liquid in the tube, a mass.
Gasses are much less stiff (more compliant, more compressible) than liquids. Air bubbles in the tube to the
transducer introduce soft spring elementsthat lower the resonant frequency of the system. If it reachesthe range of
the frequencies present in the signal, then resonant peaks will appear and information above that frequency will be
lost.
ln the caseof the arterial pressurewave for a human, the frequency range is from DC to about 40Hz'
Note also thag for it to sense pressure,a small quantity of fluid must flow in and out of the transducer. There is,
therefore, a flowrate along the catheter and tube. Restrictions to this flow such as a small diameter or partially
blocked catheter will filter out the highest flowrates first...those associatedwith the high frequency components of
the signal.
Continuous flushing device. ,
Blood pressuretransducersmay also contain a port for connection to a continuous flushing devicc. This consists of a
'The
flushing port
saline bag, in a pressurisedcontainer, such that the fluid is supplied at a pressureof 300 mmHg.
on the tranducer contains a restrictor, which drops nearly all of this pressureand allows a flowrate of about 3ml/hour
into the line. The high pressure from the saline bag is, therefore, not seen by the transducer. The restrictor may,
however, be bypassedperiodically, which applies the saline bag pressureto the line in order to flush the line after
taking a blood sample.This results in a much higher flow rate.
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